Thermal Energy Every great advance in science has issued from a new audacity of imagination ~ John Dewey (1859-1952) CHAPTER 5 Thermal energy is the energy associated with heat. Although the concept of heat is not new, its formal understanding only became clear during the nineteenth century when it was shown that heat is the result of the motion of molecules—a concept that laid the foundation for the laws of thermodynamics. In this chapter, we will give formal definitions of heat and temperature and explain how heat can be transferred as a result of a temperature difference. Then we will discuss various modes of heat transfer and the laws of thermodynamics. Finally, we will show how these laws can be used to design practical devices and more efficient machines. Heat and Temperature Two of the earliest words that children learn are “hot” and “cold”. They quickly learn to avoid touching hot stoves and getting too close to fires. They also learn to protect themselves with warm clothes in wintry weather and to stay in the shade on hot summer days. In spite of this common perception, precise definitions of heat and temperature are no less elusive than most abstract concepts in physics. As we shall soon learn, heat is a form of energy that flows from a hot object to a cold object as a result of a temperature difference that exists between them. Heat Heat is perceived as something which produces a sensation of warmth. The sensation will, of course, be stronger in higher temperatures. There cannot be any heat transfer between two objects that are at the same temperature. The amount of heat transferred depends on the temperature difference and the conductivity of the path between the two objects; the direction of heat flow is always toward the cooler object. Earlier philosophers considered heat as a substance that was passed from hot objects to colder ones. This heat fluid was known as phlogiston (meaning flammable in Greek), which was thought to have a mass and the ability to flow in and out of objects during burning; it was considered to be the soul of matter. The concept was refined after Lavoisier an eighteenth century French chemist, showed that mass is a conserved quantity and does not change when a substance undergoes a chemical reaction. The new substance was called caloric, a mass-less fluid thought to flow from hot to cold objects. It was not until the middle of the nineteenth century that Thompson and Joule showed that this theory is also wrong; heat is not a substance, but rather a manifestation of motion at the molecular level (kinetic theory). For example, when we rub our hands against each other both hands get warmer, even though initially they were at the same cooler temperatures. If the cause of the heat were a fluid, then it would have flowed from a (hotter) body with more energy to another with less energy (colder). Instead, the hands are heated because the kinetic energy of motion (rubbing) has been converted to heat in a process called “friction”. Question: W hy was the concept of heat as a fluid so well received for so many centuries? Answer: Because it met all the human notions of how a fluid should behave. It could pass from one body to another, similarly to the flow of water in a river or a pipe. When a hot object comes into contact with a colder one, the hot object cools and the cold one gets hotter as if some substance were passing from one to the other. Heat is also capable of running a steam engine in the same manner that water could turn a waterwheel. Temperature The word “temperature” seems so familiar to most of us that we often take it for granted. While our built-in senses do provide us with a qualitative characterization of temperature, our senses can often be unreliable and misleading. On a cold winter day, for example, an iron railing seems much colder to the touch than a wooden fence post, yet both are the same temperature. This “deception” by our senses arises because iron conducts heat away from our fingers much more readily than wood does. Similarly, if you place one hand in a bowl of warm water and one hand in a bowl of ice water, then remove both hands from the bowls, the hand from the hot water feels cold, while the hand from the cold water feels warm, though both hands are really feeling the same air temperature. Until Scottish scientist Joseph Black (1728-1799), a founder of modern chemistry and a pioneer in the study of heat, no one established a distinction between heat and temperature. Black distinguished between the quantity (caloric) and the intensity (temperature) of heat. Temperature Scales Thermometers are commonly used to measure temperatures. To be useful, thermometers have to be calibrated—which may be done by measuring the rise of a column of fluid (such as water, alcohol, or mercury) as it expands when exposed to an environment. Referring to the fluid analogy, temperature as a measure of coldness or hotness of an object could easily be 86 Chapter 5 - Thermal Energy interpreted as the “height” of the caloric fluid within the thermometer. Using two reference points makes it possible to divide the distance between them into a number of equal intervals. The first thermometers were divided into 360 parts, like degrees of a circle (thus the term “degree”). In 1708, Gabriel Fahrenheit used spirits as the fluid and a mixture of ice, water, and salt, the lowest attainable temperature in a laboratory setting at the time as the zero mark. The second reference point he used was the temperature of the human body, which was assigned the value of 96º. The choice of 96º is believed to be due to the fact that it is divisible by 2, 3, 4, 8, 12, 16, and 32. Today, the Fahrenheit scale uses the freezing and boiling points of water as 32º and 212º. According to this scale, body temperature is 98.6ºF. Swedish astronomer Anders Celsius, who assigned the numbers 0 and 100 to the freezing and boiling points of water, used what is known as the centigrade scale. In 1948, the International Committee on Weights and Measures adopted this scale as the temperature standard, calling it Celsius in honor of its inventor. As we will see when we introduce the laws of thermodynamics, there is a lower limit to the temperature that can be reached. This temperature, called the Zero Absolute Temperature (-273.15º Celsius or zero kelvin), is understood to be the temperature of a perfect crystalline lattice. There is no upper boundary to temperature, although the highest predicted temperature is 1038 K which was the suspected temperature at the very beginning of the creation of the universe, the Big Bang. Sustained fusion reactions require a temperature of 108 K , and thermal plasmas occur at temperatures of 104 to 106 K . Table 5-1 gives formulas for converting temperatures between Celsius, Fahrenheit, and Kelvin scales. Thermal Properties Table 5-1. Temperature Conversion Formulas Equations for converting between Celsius (C), Fahrenheit (F), and Kelvin (K) temperature scales o o F = 1.8 oC + 32 K = oC + 273 (i) (ii) (iii) C = (oF – 32) / 1.8 Different substances have different abilities to retain or transport heat. For example, some materials, like Styrofoam and cork, are better insulators than aluminum, and some materials, like sand and brass, warm more quickly than grass. Thermal properties of materials are best understood by three quantities: heat capacity, specific heat, and heat conductivity. The heat capacity of a substance measures its ability to retain heat. It is defined as the quantity of heat required to raise a substance by one degree in temperature. Water has a higher heat capacity than sand because it takes more heat to warm up by the same amount than sand does. In other words, for the same amount of heat, sand temperature raises more than water temperature. Closely related to heat capacity is specific heat, which is the heat capacity per gram of substance. Thus, a bigger object will have a greater heat capacity, but the same specific heat. The more loosely the components of a solid are held together, the higher the substance’s specific heat. Graphite has a higher heat capacity than diamond because 87 diamond’s lattice structure is more tightly bound than the graphitic structure of carbon. In SI units, specific heat is expressed in kJ/kg.K. Question: W hich do you think has the higher specific heat, lead or water? Answer: Lead atoms are over three times heavier than water molecules. Thus, a given quantity (by mass) of water has more molecules than the same quantity (by mass) of lead. Consequently, a given quantity of heat is distributed among fewer lead atoms than water molecules. This means that lead will experience a greater temperature increase and thus has a lower specific heat. Question: Licking a silver spoon that’s been sitting in a very hot cup of coffee probably won’t burn your tongue, but a spoonful of the same hot coffee dropped on your tongue could leave a blister. Why? Answer: The heat capacities of water and silver are 1 and 0.06 cal/ g.°C, respectively. That is, silver contains much less heat energy than water at a given temperature. Thermal conductivity is a measure of a body’s ability to conduct heat. Table 5-2 gives values of thermal conductivity for several materials in order of their conductivity. As can be seen from this table, silver is a very good conductor of heat, with copper not too far behind. Air appears towards the end of the list, meaning it is a very poor conductor, but an effective insulator. Table 5-2. Thermal Conductivities of Selected Materials, W/m.K (values at 20ºC, unless otherwise stated) Good Conductors Diamond Silver Copper Aluminum Iron Lead Stainless steel Granite Average conductors Poor conductors (good insulators) 2.20 Brick, insulating 1.70 Asbestos 1.50 Fiberglass 1.00 Glass wool 0.60 Styrofoam 0.59 Air (dry) 0.20 Silica aerogel 0.16 Vacuum 0.150 0.090 0.040 0.040 0.033 0.026 0.004 0 2,000 Ice (0ºC) 429 Concrete 400 Soil 220 Glass 80 Water 35 Epoxy 14 Body fat 3 Snow Heat Transfer Heat transfer is a result of temperature variation within a medium and occurs through one or more mechanisms of conduction, convection, and radiation. Conduction Conduction is the transfer of heat from molecule to molecule through 88 Chapter 5 - Thermal Energy a substance. If a steel bar is temporarily heated at one end, its molecules become agitated and move faster than neighboring molecules. When fastmoving molecules collide with slower molecules, energy is transferred from faster to slower molecules. The chain reaction moves along the bar until its temperature is uniform. While conduction does take place in gases and liquids, its effects are most pronounced in solids. The closer the molecules are packed, the easier conduction is. Heat transfer via conduction increases in materials with a greater heat conductivity and larger temperature gradients. Question: W hy do animals living in freezing climates often burrow into the snow to sleep? Answer: In addition to furs and thick skin, air spaces in the snow help animals protect themselves in such harsh weather. Snow, a poor conductor, slows the loss of body heat. In freezing weather, an igloo would provide a warmer shelter than would a wooden shack because the snow and ice of the igloo are better insulators than wood. Question: How do gloves protect our hands in the cold? Answer: The temperature difference between hands (37°C) and outdoor air (say 0°C) is the same whether we wear gloves or not. However, with gloves heat follows a path of greater resistance, and the rate of heat loss from our hands reduces. Convection Convection is energy transfer by bulk motion. Unlike conduction, which is a microscopic phenomenon, convection involves the macroscopic interchange of energy between two mediums. Convection is most prominent in gases and liquids, where the distances between molecules are too large for conduction to be effective. Convection can be classified as natural or forced. In natural convection, fluid motion is a result of a density gradient, whereas forced convection is mainly due to a pressure gradient. Hot air balloons rise as a result of natural convection because they contain hotter, lower-density air. Helicopters are lifted by forced convection resulting from the pressure difference across their propeller blades. Dogs often pant to get rid of excess heat by forced convection. It should be noted that heat transfer by convection and conduction are closely linked. Consider for example, the cooling of a hot plate by blowing air over it. As the cold fluid replaces the warmer fluid (convection), more heat is conducted away from the plate; the process continues until the surface temperature approaches that of the fluid, in this case the surrounding air. A fan placed in front of a car radiator functions in a similar manner. In buildings, convection losses are due to air infiltration through the cracks, windows, and other openings in walls. Additional losses occur due 89 to air movement inside and wind motion outside the exterior glasses and windows. In a typical building infiltration losses are the most significant and are comparable to losses by conduction. Common insulation materials such as fiberglass, rigid boards, cotton, and feathers work by creating tiny air pockets that slow down the convection flow of heat. Convection is not only important at the local level, but also plays a role in large-scale movements of the atmosphere. The major winds are convection currents driven by temperature differences caused by nonuniform heating of the earth by solar radiation. The winds, in turn, drive the ocean currents. Question: To keep a body warm in a cold winter, would it be more beneficial to wear two layers of light clothing or one layer of clothing twice as thick? Answer: Two layers will work best because there is always some air trapped between the layers, providing additional insulation. Question: Is it best to add creamer to coffee immediately after the coffee is poured or to add it right before drinking the coffee? Assume that coffee is most desirable when it is hot. Answer: Creamer should be added as soon as the coffee is poured. Two effects are of importance: First, creamer makes coffee lighter in color, reducing its emissivity and heat loss from radiation. Secondly, adding creamer sooner decreases the temperature difference between coffee and the environment, reducing the rate of conductive and convective losses. Radiation Radiation is the transport of energy by photons of light migrating from a hotter to a colder surface. Unlike conduction and convection, both of which require a material medium to transport heat energy, radiation transports energy via electromagnetic waves of different wavelengths , even in a vacuum (Figure 5-1). Wavelength is the distance between two successive crests or troughs in a wave; the shorter the wavelength, the higher its energy is. No matter what the wavelength is, they all travel at 300,000 kilometers per second, the speed of light. The most energetic radiations are gamma rays and x-rays. Gamma rays come from the nuclei of certain atoms with wavelengths smaller than the size of the atom; x-rays come from the innermost orbits of electrons. The least energetic radiations are from radars and radio waves, with wavelengths that can exceed several meters or kilometers. R adiation at wavelengths shorter than 0.3 microns (high intensity ultraviolet) is dangerous to humans. Its effects can range from simple sunburn to cancer and death. Photons at these short wavelengths are 1 Hz Power Lines 60 Hz Radio Navigation 1 kHz 1000 km AM Radio Shortwave Radio TV and FM Radio Cell phone Microwaves Radar 1 GHz 1 MHz 1 km 1m 1 THz 1 mm Infrared VISIBLE Ultraviolet 1 PHz 1 µm 1 EHz X-rays 1 nm 1Aº Gamma-rays Frequency Wavelength Figure 5-1 Electromagnetic wave spectrum 90 Chapter 5 - Thermal Energy sufficiently energetic to break bonds in molecules of living matter. Fortunately, most are filtered out by earth’s atmosphere. Wavelengths between 0.3 and 0.4 microns (near ultraviolet) are weakly absorbed by clouds and dust in the atmosphere, while the rest reach the earth’s surface. Microwaves have frequencies close to the resonance frequency of water molecules, and therefore, readily absorbed by water molecules, a feature exploited in microwave ovens for the rapid heating of food. Radar, TV, and radio waves have very long wavelengths (from many meters to kilometers) and thus are of very low energy; they are mainly of interest in communications. The atmosphere is largely transparent to rainbow colors, which make up visible light and cover wavelengths in a very small range from only 0.4 microns for deep violet to 0.7 microns for bright red. Although earth’s atmosphere is transparent to visible radiation, it is virtually opaque to Wind Chill Factor FYI ... A ir circulation promotes cooling for two basic reasons. It removes the warmed layer of air blanketing our bodies, which could potentially (in still air) act as insulation against conductive heat loss, and it promotes cooling by evaporation. While some cooling can increase our comfort level, a strong wind can also create an unbearably chilling environment. On a windy day, air currents cause greater heat loss, as the warmer insulating air layer next to the body is continuously replaced by cooler, ambient atmosphere. The effect of wind on how cold we feel is conveniently expressed in terms of the wind chill factor (WCF). Wind chill factor describes the rate of heat loss from exposed skin due to the combined effects of wind and cold. The higher the wind speed, the higher the rate at which heat is removed from the body and the lower the body temperature becomes. It must be emphasized that WCF expresses an actual cooling rate and not simply some illusory sensation, as anyone living in the “windy city” of Chicago will attest to. For instance, the figure below shows that for an air temperature of 10oF and a wind speed of 15 mph, the cooling power of the moving air is equivalent to that of still air at -7oF. The wind chill factor is a good way to determine the potential of frostbite or hypothermia. Image courtesy of NOAA / National Weather Service. Different contours represent frostbite times. Question: At wind speeds of 4 mph or lower, wind chill temperature turns out to be warmer than the actual temperature. How do you explain this? Answer: When the wind blows at low speeds, our body warms the layer of air next to our skin. Since air is relatively still it acts as insulation, protecting us from colder air farther away from the warmth of our bodies. 91 Figure 5-2 Thermal image of a man. The hotter regions (bare skin) are lighter in color, and cooler spots (tee-shirt, arm pits) are darker grey. The choice of shades of grey is arbitrary and does not imply a physical significance. Photo courtesy of Thermotronics Inc., Brazil. infrared radiation, which has wavelengths longer than 0.7 microns. As we will see in the next chapter, this is the main property responsible for the atmosphere’s behavior as a greenhouse; letting solar radiation in while trapping terrestrial infrared radiation results in the global warming phenomenon. Whether a body emits energy at one wavelength or another depends on its temperature and surface properties. An object at room temperature, say 20°C, emits nearly all its energy in infrared. The human body at ordinary temperatures also emits in the infrared region. In fact, 98% of the radiation from a bare human body ranges from 4.78 to 75 microns in wavelength. Using a special infrared camera it is possible to “see” a human body or a passing car in total darkness. The image will not look like what we see with our single lens cameras, but will be a contour map of constant temperature regions. An infrared (thermal) image of a man wearing a teeshirt is shown in Figure 5-2. Question: If human beings emit infrared, why do we see them in “visible” light? Answer: W hat we see is not emitted light, but the reflection of light from other sources (sunlight, fluorescent light, etc.). This is why in the absence of a light source (darkness) there is no light reflected to the eye and a person cannot see or be seen. Unlike conduction and convection losses that increase with temperature differences between cold and hot objects, radiation losses increase as the differences of the temperatures to the fourth power (T4hot - T4cold), and become dominant only for very high and very low temperatures. In buildings, radiative losses are most significant when the surrounding terrain is either much colder or warmer than inside. Roofs can radiate a substantial amount of energy to the cold night sky. They also provide a low-resistance path to solar heat during the summer months. Window glass is much colder than adjacent walls during the winter, causing internal heat, such as heat released by the occupants or heaters, to migrate toward windows. This results in a larger temperature difference across the glass layer and causes more heat to escape through windows. Double-glazing 92 Chapter 5 - Thermal Energy the windows, closing the curtains, and adding additional insulation in the walls and attic can significantly reduce these losses. Question: You have probably experienced colder room temperatures in the winter when drapes are not closed, even though the thermostat records air temperature that should be comfortable. Why? Answer: Glass is transparent to radiation in the visible range, but is opaque to infrared. The radiation from cold glass windows to you is much less than yours to the window. Question: You can easily feel the heat from the sun through a glass window, but behind a sheet of glass you do not feel much heat from a fireplace. Why? Answer: Common window glass is transparent to the wavelengths of radiation between 0.3-2.5 µm. A large portion of solar radiation falls in this range, allowing both sunlight and solar heat to pass through. Flames, however, emit in wavelengths in excess of 2.5 µm, the region where window glasses are practically opaque. Thermodynamics Thermodynamics is made up of two Greek words: therme (heat) and dynamis (power). It is the science that describes the dynamics of heat and how it can be converted to power. Thermodynamics is a phenomenological theory derived from four very simple observations: 1) heat cannot flow between bodies of the same temperature; 2) heat and work are just two different forms of energy; 3) heat always flows from a hot body to a cold body; and 4) there is a temperature (called zero absolute temperature) that can never be reached. These observations have been refined and reformulated as the zeroth, first, second, and third laws of thermodynamics. These laws are important because they provide the basis for designing many machines and modern devices that change heat into work (such as an automobile engine or a power plant) or turn work into heat or cold (such as an electric heater or a refrigerator). Equilibrium (The Zeroth Law of Thermodynamics) Two objects at the same temperature are at equilibrium and remain at equilibrium until the temperature of one of the objects changes. On the other hand, if we put two objects of different temperatures next to each other, one object heats and the other cools until both bodies reach the same temperature. The zeroth law is considered obvious and will not be discussed any further. The Zeroth Law of Thermodynamics: Objects at equilibrium must have the same temperatures. 93 Conservation of Energy (The First Law of Thermodynamics) The principal of conservation of energy, or the first law of thermodynamics, implies that the energy of a system does not change as it goes from one state to another; only its form changes. The First Law of Thermodynamics: Energy can be neither created out of nothing nor destroyed into nothing, but it can be changed from one form to another. For example, a glass resting on the edge of a table has a certain potential energy. If the glass is knocked off the edge, its potential energy is converted to kinetic energy as it accelerates towards the ground. When the glass hits the ground the kinetic energy is converted to light energy (sparks), sound energy (a bang), thermal energy (heat), and chemical energy (the glass breaks). The first law of thermodynamics is the basis of all energy conversions from one form to another. Many of our biological activities are geared to perform these energy conversions. For example, during digestion, food molecules are broken down into progressively simpler molecules (chemical-chemical conversion); in the process some of the chemical energy stored in those molecules is converted to the thermal energy necessary to maintain our body temperature. Numerous practical devices have been designed that accomplish useful tasks through the conversion of energy from one form to another. Table 5-3 gives examples of different kinds of energy conversions. Question: If energy can be neither created nor destroyed, how can people claim that there is an “energy shortage”? Answer: Terms such as “energy shortage” and “energy waste” are misnomers. While total energy must remain constant, useful energy — that which can be used as fuel or perform work— may be in short supply. According to the first law, energy can never be wasted; it may only be converted to a form not readily usable to us. This is explained more when we talk about the second law of thermodynamics. Question: If energy can be transformed, what is it transformed into? Table 5-3. Examples of Different Kinds of Energy Conversions FROM/TO MECHANICAL THERMAL CHEMICAL ELECTRICAL LIGHT MECHANICAL Bicycle, Gearbox Gas turbines Rockets, thermal engines Electric motor, Loudspeaker Galvanometer THERMAL Friction Heat exchanger Food, Fires Resistor heater Solar collector CHEMICAL Cigarette lighter Pyrometer Metabolism Electrolysis Photosynthesis ELECTRICAL Wind generator, Microphone Thermocouple Battery, Fuel cell Transformer Solar cell LIGHT Sparks Luminescence Candle Light bulb Fluorescence 94 Chapter 5 - Thermal Energy First Law and Nuclear Reactions FYI ... I n the century and a half since the first law was formulated, the law has come into question on occasion. For example, nuclear reactions seemed to occur in violation of this law. Thanks to the pioneering work of Einstein and others, the first law continues to be upheld-- at least so far! Answer: Although we often talk about transformation of energy, we should note that the nature of energy has not changed. We are only talking about its manifestation from one form to another. Chaos and Disorder (The Second Law of Thermodynamics) Countless processes have a preferred or “natural” direction. Heat flows spontaneously from hot objects to cold ones. Water will flow from high mountains toward rivers. Air rushes out of a punctured rubber balloon. Smells tend to diffuse outward to span greater distances. Humans grow older by the minute. When a house is left unattended, it quickly becomes disorganized. All these processes have one thing in common; they all tend to become more dispersed (chaotic). This is one statement of the second law of thermodynamics, which can be generally stated as: The Second Law of Thermodynamics: All natural processes tend to go from order (concentrated) to disorder (dispersed). More simply put — events happen in a certain direction. Although many people think the second law of thermodynamics must only be of interest to physicists, engineers, and those who deal directly with heat and energy, the second law has far-reaching consequences not only in predicting the fate of the universe, but also in all aspects of our daily lives. The second law gives us guidelines for what we can and cannot do. It tells us how to design better machines and provides us with a blueprint for using our resources more efficiently. In short, it gives us a sense of direction. Question: It is often said that it is impossible to obtain negative absolute temperatures. Why? Answer: Because absolute zero is the state where all molecular motion ceases and the complete order is achieved. Negative temperatures imply better than perfect order! Question: W hat does the second law tell us about the ultimate fate of the universe? What should we expect after a severe earthquake? After dropping a glass cup from the edge of a table? Answer: According to the second law, the universe will continue toward complete disorder (thermodynamic equilibrium), where all non-uniformities in temperature, electric potential, pressure, etcetera, vanish and eventually reach a heat death. Accordingly, it predicts that earthquakes flatten buildings – decreasing order. Similarly, dropping 95 a glass cup off a table edge will likely break it into many pieces, increasing the disorder. Remember that an unbroken glass cup, by the virtue of the careful positioning of the atoms in a lattice structure, is highly ordered. Entropy Measuring the temperature of a room or the pressure of the tires of a car are probably easy and routine tasks. All that is needed is a thermometer or a pressure gauge. But how can we measure chaos? Is there a way to quantify how much dirtier my room is than yours? Ludwig Boltzmann (1844-1906), an Austrian scientist, attempted to do exactly that. The result of his studies is summarized in a single equation that defines entropy (from the Greek root meaning transformation) as a measure of randomness, or the total number of configurations that a system can assume. The concept of entropy is closely intertwined with the second law of thermodynamics in the sense that processes happen such that the total entropy of the universe is constantly increasing. When dealing with energy, the second law implies that it must flow from the one with the least amount of disorder (lower entropy) to the one with a higher amount of disorder (higher entropy). Question: It is an easy task to mix two tablespoons of salt and pepper. It takes quite a bit of work, however, to separate a mixture of salt and pepper into its constituents. Why? Answer: Salt and pepper by themselves are relatively orderly, but when mixed, disorder will increase considerably. Separating salt and pepper requires work because we need to create order by reducing the mixture’s entropy. Question: Visualize a deck of cards where all the cards are arranged according to suit and rank. How does the entropy change if the deck is shuffled a few times? Answer: W hen suits are to be arranged in some orderly manner, rearrangement is limited. There are a great number of ways that a deck can be rearranged if a particular order is not demanded; the entropy is thus increases. Question: An electric heater dissipates electrical energy into heat (and some light). What are the implications of the first and second laws of thermodynamics? Answer: The first law assures that electrical energy is completely converted to heat (and light). The second law implies that the energy flow is from order (flow of electrons in the electric coil) to disorder (random motion of heated air molecules in the room). Question: W hen a gas balloon is heated, it expands. What happens to the entropy? 96 Figure 5-3 With the aid of a few hundred pounds of dynamite, demolition experts caused this hotelcasino in Las Vegas to go from an ordered state (lower entropy) to a disordered state (higher entropy). Chapter 5 - Thermal Energy Living Organisms and the Second Law of Thermodynamics Digging Deeper ... A ccording to the second law of thermodynamics, nature always prefers chaos to order. Living organisms which formed from simple cells to complex beings seem to violate the second law in a big way. It should be noted that the second law applies only to isolated systems. Isolated systems cannot exchange energy or matter with their environments. The only truly isolated system is the Universe itself. Earth is not an isolated system because it exchanges energy with the sun and the surrounding atmosphere. Living organisms exchange both energy (heating or cooling by the environment) and mass (eating, breathing, and sweating) and therefore are not isolated systems. The sanctity of the second law is thus preserved! Qin Qout A plant is an example of a heat engine which transforms light energy into chemical. Answer: As the balloon expands, it opens more room for gas molecules to occupy. In other words, the possibility that gas molecules take different configurations increases. Thus the balloon’s entropy increases. Absolute Temperature (The Third Law of Thermodynamics) As substances cool, their molecules move with less speed and their kinetic energy decreases. Actually, it can be shown that the kinetic energy of particles is directly proportional to the temperature. To rephrase, temperature can be seen as a measure of the kinetic energy of particles. It is therefore easy to understand that at temperatures of absolute zero, all molecular motions stop, and entropy approaches zero. The Third Law of Thermodynamics: There is a temperature so low that it cannot be reached. This temperature is called absolute zero kelvin (-273.15oC) Thermal Devices The first law of thermodynamics showed that we could convert energy from one form to another. When its brakes are applied, a car will slow down because of friction. As a result, both the tires and the road become a bit warmer. In this example, work has been turned to thermal energy or heat; therefore, work and heat are quantitatively the same. Experience tells us the reverse, cooling the tires and road to move the car backward, is not possible. This shows that thermal energy (heat) and mechanical energy (work) are qualitatively different - work can be turned entirely to heat, while the reverse is not true. This simple observation is a direct consequence of the second law of thermodynamics, which states that processes can occur naturally in one direction and not the other, although energy expenditure is exactly the same in both cases. One of the applications of thermodynamics is in designing devices that transform one form of energy to a more useful form. Of course we wish to design these devices using the least amount of energy and with the highest 97 Combustion Chamber at TH = 2000°C Required Input Qin efficiencies possible. The first law of thermodynamics requires a minimum amount of energy to achieve a task. The second law of thermodynamics puts a limit on how efficient a device can be. From a theoretical standpoint, a device is most efficient (ideal) when it operates with no frictional losses; in reality, most systems have much lower efficiencies. Some examples of thermal devices we use or are impacted by in everyday life are engines, power plants, refrigerators, heat pumps, and air conditioners. In all these devices, some form of energy (fuel) is consumed. W hether used in automobiles or jet aircrafts, heat engines convert part of this energy to shaft work that eventually runs the vehicle (Figure 5-4a). Power plants work in a similar fashion, but their work output is mainly in the form of electricity. Refrigerators, air conditioners, and heat pumps work in essentially the reverse direction; they use fuel energy to “pump” heat away from the space we want to cool or “pump” heat into the space that we want to heat (Figure 5-4b). No matter what the application, part of the energy is always discarded as waste energy into the surrounding atmosphere. In other words, it is impossible to build devices that convert 100% of the input energy into useful forms. Furthermore, because there are always some frictional losses, actual efficiency is always less than the maximum theoretical efficiency dictated by the laws of thermodynamics. Table 5-4 shows the typical efficiencies of several machines. Internal Combustion Engines Internal combustion engines are one example of thermal heat engines with widespread applications in power generation as well as in transportation systems. Basically, these devices burn a mixture of hydrocarbon fuels with the ambient air inside a combustion chamber (cylinder) to produce power. The power is transmitted through a shaft which can run a generator, drive the crankshaft of an automobile, or provide thrust to propel a jet aircraft. Among the most common internal combustion engines are gasoline and diesel engines and gas turbines. These devices are discussed in detail when we cover transportation systems in Chapter 14. Efficiency HEAT ENGINE Qout Wnet, out 25°C Desired Output Exhaust at TL = 100°C (a) Warm environment at TH = 25°C Required Input Wnet, in 25°C Desired Output QH Refrigerator QL Cold refrigerated space at TL = 0°C (b) Figure 5-4 Heat engines and refrigerators Table 5-4. Typical Efficiencies of Some Complex Machines Machine Automobile Steam engine Steam locomotive Steam turbine Gas turbine Efficiency 12-15% 50-75% 5-10% 30-40% up to 40% Wouldn’t it be great if we could build a machine which puts out more work than we put into it? This machine would constantly create new energy and we would never have an energy shortage. If that were possible, we could build machines that, once started, did not need an additional expenditure of energy. This would be ideal, and many people have dreamt of making such machines. These machines, commonly known as “perpetual motion machines” (PMM), could operate forever. Sound too good to be true? It is. In the real world, all machines produce less work than the energy that goes into them. Useful energy is always lost as heat. That’s the reality but, as shown by those who attempt to design PMMs, not everybody chooses to accept it. Unfortunately, the first law of thermodynamics precludes constructing such machines. 98 Chapter 5 - Thermal Energy Cash vs. Gift Certificate FYI ... T he difference between work and heat can be compared to that between cash and gift certificates from a major retail store. Cash and gift certificates have the same nominal value, in the same way that work and heat are quantitatively the same (1st law). The cash is of a higher quality because it has more diverse applications. Similarly, work is of a superior quality because it can be used in more ways. When purchasing an item from the retailer, a gift certificate has the same utility as cash. The same is true when work is used to perform a task that can be accomplished equally well by heat. For example, a resistance heater uses electricity (a form of pure work) to heat a house — a task that could easily be done using a gas heater. This does not mean that gift certificate is of no value outside the retail store, as it can be traded (for example, paying for the gas, but at a smaller amount than its face value). The same can be said for heat; we can use heat to produce work (heat engine), but at less than 100% efficiency. Question: Why is it more advantageous to use a gas heater over an electric heater for heating a room? Answer: Remember that most electricity is generated in power plants by burning some form of fossil fuels. In the process, 70% of energy is lost to the atmosphere (see “Heat Engines”). Additional losses occur during transmission, before the electricity is converted back to heat - a task that could be accomplished directly by burning gas in a gas heater. Using electricity for heating purposes is similar to using cash when you could have used the gift certificate instead! Not only is the construction of such engines impossible, the second law of thermodynamics prevents the construction of engines that can convert “all” or “nearly all” of the heat input into useful work. This can be understood by noting that heat is a less ordered form of energy than work and complete conversion of heat to work would accompany a reduction of entropy (in violation of the second law), which is impossible. Many inventors have proposed (and still propose) devices that violate the first and second laws of thermodynamics. Some, like Maxwell,1 do so from a purely philosophical standpoint, but many have actually dared to propose such machines as practical devices.2 Many have even received patents and accumulated great wealth from their “inventions”. As you may have guessed, nobody was ever able to produce a working prototype. Question: One of the consequences of the second law is that whenever energy is transformed from one form to another, at least some of the energy changes to a more dispersed form such as heat (recall that heat is a less ordered form of energy). Is it possible to design devices that transform energy in the opposite direction, i.e. take it from a dispersed form to a more concentrated (ordered) form? Answer: The second law only precludes going from disorder to order for isolated systems. Many practical devices are not isolated and thus do not have to follow this restriction. For example, an air conditioner works by removing heat from a room and dumping it outside at a higher temperature. In this case we are re-concentrating energy. To do so, however, we need to spend even more energy in the form of electricity. 1 2 James Clerk Maxwell (1831-1879) was a Scottish mathematician and physicist, most known for his theoretical formulation of laws of electromagnetism. A ngrist, S. W, “Perpetual Motion Machines,” Scientific American, 218:114-122, January 1968. 99 Question: Our solar system has been moving around the sun for a very long time and does not seem to slow down. Can the motion of the solar system be considered an exception to the second law? Answer: If we look at the grand scale, motion of the Universe indeed conforms to the rules set out by the laws of thermodynamics. Energy is continuously poured in, externally and on a massive scale, to power the motion of all the galaxies and the motion of all that is within them. Even the solar system has to adhere to the laws put forth by nature! The Ceiling on Efficiency In an attempt to improve the efficiency of the early steam engine, the French scientist Sadi Carnot proposed an ideal engine that works between two reservoirs at different temperatures. Heat is removed from a source at temperature Thot, part of which is discarded to a sink at temperature Tcold; the remainder is supplied as work. The best this engine can do is to achieve a loss of entropy from the source that just balances the gain in entropy by the sink. The net entropy production will then be zero. Under such ideal conditions, the efficiency of the engine is the maximum attainable and is equal to T ηideal = ηmax = 1- cold (5-1) Thot Tcold and Thot are temperatures of cold and hot reservoirs and must be expressed in kelvin. Kelvin temperatures are calculated by adding 273 to temperatures expressed in degrees Celsius. Question: An inventor claims to have designed a cyclic engine that takes 1,000 Joules of heat and converts it entirely to work. How would you rate this claim? Answer: His claim is impossible. The engine removes some heat from a reservoir, resulting in a drop in its entropy. Since work is perfectly ordered, no additional entropy is created. The net result is a decrease in the total entropy of the universe, in opposition to the principal of increasing entropy as stated by the second law. Example 5-1: The same inventor comes back a few months later after having worked on a second engine. His new claim is that his engine can remove 1,000 J of heat from a source at 500 K, dump 400 J to a sink at a temperature of 250 K, and use the remaining 600 J as work to run a shaft. Would you invest in his company? Solution: The ideal efficiency of an engine working between these two temperatures is 1-250/500 = 0.50; at best only 50% of the input energy can be converted to work. The proposed engine has an efficiency of 600/1000 = 0.60, higher than the ideal efficiency of 50%, which is an impossibility. Because of frictional losses, we can expect actual efficiency to be even lower than 50%. Once again, his claims cannot be realized. 100 Chapter 5 - Thermal Energy Hurricanes Digging Deeper ... A hurricane (called “cyclone” in the southern hemisphere) can be viewed as an elegant example of nature’s Carnot heat engine. It draws heat from the ocean by evaporating the water and turning it into steam, releases some of it to the atmosphere via radiative cooling and condensation, and does work during this process.i The Coriolis force converts the upwards suction of the air to spiral motion. i Emanuel, K. A. 1987. “The Dependence of Hurricane Intensity on Climate.” Nature. 326: 483-485. i First-Law and Second-Law Efficiencies Real engines can never achieve the ideal efficiencies given by Carnot. First, real engines have always frictional and conductive losses that cannot be completely eliminated, thus limiting their maximum performance. Second, depending on its intended end use, a device may not be able to utilize the full potential of energy used to operate.3 To quantify these limitations, two types of efficiency are defined. The first-law efficiency is defined based on the first law principle of conversion of one form of energy to another, without any consideration to the quality of the energy resource. First-law efficiency is input/output efficiency, i.e. the ratio of energy delivered in a desired form and the energy that must be expended to achieve the desired effect. It does not differentiate between the qualities of the energy sources. The first-law efficiency can be less than (heat engines), equal to (friction), or greater than (refrigerator) one. In the latter case, it is commonly referred to as “the coefficient of performance” (see below). Question: W hat is the first-law efficiency for a heat engine? For an electric heater? For an electric motor? For an electric light bulb? Answer: A heat engine is a device that converts chemical energy (fuel) to mechanical work. Therefore, the first-law efficiency is the ratio of shaft work to heat input. Typically, first-law efficiencies of 25-30% can be achieved for automobile engines. An electric heater is a device for converting electrical energy to heat; in this case the first law efficiency is the ratio of heat given off to electric work needed to operate the heater (compare this to the first law efficiency of the heat engine!). Aside from small radiant losses through the heating coil, electric heaters are very efficient devices for their stated purpose and efficiencies close to 100% are achievable. Electric motors lose some energy through friction and coil heating and are generally around 90% efficient. Incandescent light bulbs are designed to convert electricity to light. A major fraction of the energy is, however, lost through heating the filament. The efficiency is rather low at around 5%. Unlike the first-law efficiency that ignores the qualities of the energy, the The students who take a more advanced course in thermodynamics will learn of a new term, “exergy ” or “availability,” that distinguishes the part of energy in a system that can be converted to work from the part that cannot (is unavailable). Unlike energy, exergy is not conserved and destroyed in all real processes. 3 101 Digging Deeper ... Gas vs. Electric (Revisited!) A t a department store you inquire about a gas heater for your house. The salesperson offers you two heaters, a gas heater with 70% efficiency and an electric heater with an efficiency of 97%. Which one would you choose? The first inclination might be to purchase the electric heater. It is more efficient, it is cleaner, and might even be cheaper. A slightly more careful analysis will reveal that the salesman is actually giving you first-law efficiencies. The electricity used to run the electric heater is coming from a gas-powered generating station with 33% efficiency. The electricity is transmitted through a power line from the power station to your home. An additional 5-10% (let’s say 10%) is lost through heating the wire (Joule heating). The overall efficiency (system efficiency) of the electric heater is then (0.33)(0.90)(0.97) = 28.8%. Assuming transmission losses of 5% through gas pipes, the first-law efficiency of the gas heater is (0.95)(0.70) = 66.5%. Gas Power Plant 33% Electric Heater 97% Heat output 28.8%% Transmission losses through wires, 90% Gas Transmission losses in pipelines, 95% Gas Heater 70% Heat output 66.5% second-law efficiency compares the efficiency of an actual device (1st law efficiency) to that of the same or a similar device operated under ideal conditions. It measures the actual energy used as compared to the minimum amount of energy needed to accomplish the same task, i.e. the second-law efficiency is the ratio of the actual efficiency to that of an ideal device. By definition, the second law efficiency of all ideal devices is equal to one, and for all real devices is smaller than 1. Question: W hat is the second-law efficiency of a heat engine? Answer: To find the second-law efficiency, we must compare the heat engine to an ideal heat engine. An ideal heat engine is an engine that does not experience any frictional losses or other irreversibilities. The second law states that this engine must be a Carnot engine with the maximum theoretical efficiency given by equation 5-1. For example, an engine operating between a combustion temperature of 1,600 K and an exhaust temperature of 400 K has an ideal efficiency of 1-400/1600 = 0.75. For an automobile with an actual efficiency of 30% (first-law efficiency), the second-law efficiency is 0.3/0.75 = 0.40. That is, the engine operates at only 40% of its full potential. Question: Air pollution is considered by many to be a direct result of incomplete (inefficient) combustion. Comment! Answer: The common assumption that air pollution results from inefficient burning of fossil fuels is not correct. When a hydrocarbon fuel such as natural gas (methane) is burned in air, the product of the reaction is a mixture of water, carbon dioxide, carbon monoxide, oxides of nitrogen, and a number of other gases in such concentrations that maximize the overall entropy. Cleaner fuels, better burners, and more 102 Chapter 5 - Thermal Energy exotic catalysts, although they increase combustion efficiency and reduce the pollutant emissions, cannot eliminate the air pollutants all together. In other words, complete combustion (of hydrocarbons), defined as burning with carbon dioxide, water, and molecular nitrogen as their only end products, is not possible and is directly in violation of the second law of thermodynamics. Thermal Power Plants As is the case for any thermal engine, thermal power plants are devices that convert heat to rotational shaft work, which can be coupled with an electric generator to produce electricity.4 Unlike internal combustion engines, where the heat of combustion comes from fuel burned inside the engine, power plants use external heat – most often from fossil or nuclear fuels. Most thermal power plants follow a thermodynamic cycle which consists of a boiler, a high-pressure steam turbine, a condenser, and a pump. Water is commonly used as the working fluid, although there are instances where ammonia and other refrigerants serve the purpose best. The cycle operates using a feed water pump to introduce water into a boiler or steam generator, where it boils and turns into high-pressure superheated steam. The superheated steam subsequently enters a steam turbine, where it is expanded and cooled to a saturated mixture of water vapor and liquid water. To close the cycle, the mixture must be turned into liquid and compressed to the boiler’s operating pressure. This is accomplished by cooling the mixture in a condenser and circulating it back into the boiler using a feed water pump. To boil the water, energy is required. The source of this energy could be fossil fuel, nuclear fuel, solar heat, or a geothermal reservoir (see Figure 5-5). Question: W hat is the advantage of recycling water (as is done in closed cycles) over discarding steam and pumping fresh water (as is done in open cycles)? Answer: Recycling the same water not only conserves water, but also saves on the cost of filtering. This is essential to avoid corrosion and prevent the buildup of mineral deposits in the system. To condense steam, it must be cooled. This is done by pumping cold water from a nearby ocean, lake, or river and diverting it to the condenser. A simple analysis shows that for operation of even a moderately sized power plant, a tremendous amount of cooling water is needed. This is the main reason that most power plants are built near a large body of water such as a river or a lake. In most instances, the water out of the condenser is hotter by 10°C or more, too hot to be returned back to its source. The thermal shock of hot water can prove especially harmful to aquatic organisms The major difference between thermal, hydroelectric and wind power plants are that in hydroelectric and wind plants, water or air flows directly through water or wind turbines, w hereas with thermal power plants a working fluid is heated to its boiling temperature before it is passed through a steam turbine. 4 103 nuclear control rods fuel rods steam Electricity hot air solar sun steam Electricity hot air Boiler P Turbine Generator cold water input P fuel Cooling tower water cold air P Turbine Generator cold water input P Cooling tower water P Condenser hot water output Condenser hot water output cold air ground ground geothermal steam Centrifuge filter gas Electricity hot air Stack Emission steam Boiler Turbine Generator Electricity hot air cold water input water P P Cooling tower Turbine P Generator cold water input water cold air P P Cooling tower Condenser hot water output Condenser hot water output cold air steam water ground ground Figure 5-5 Thermal power plants consist of a boiler (or steam generator), a steam turbine, a condenser and a recirculating pump. Water boils in a boiler and turns into superheated steam. Steam will then expand in a steam turbine and deliver shaft work. The steam is condensed back to liquid water before being pumped into the boiler, beginning the cycle again. whose survival depends on a narrow range of temperature fluctuations.5 To safeguard fish and other marine habitats, there are regulations that require the condenser water to be cooled in a spray pond or a cooling tower before being returned to the lake or river from which it came. Spray ponds are large, shallow bodies of water. Water from the condenser is sprayed across the large surface of the pond, where it is cooled by evaporation. Spray ponds are normally used in areas of low humidity and where land is available. Cooling towers can be either wet or dry. Wet cooling towers are similar to spray ponds except that water is passed through coils which look like a shower head. As water is dripped down, it is cooled by the ambient air and is collected in a basin. Heat is transferred from water to the ambient air, where it stays (Figure 5-6). The air is usually either sucked out by giant blower fans placed on top of the cooling tower (forced draft) or flows naturally upward to replace the less-dense warm air, which is rising out of the tower (natural draft). Wet towers are large and use two to three times as much water as cooling ponds. Furthermore, many people find the towers aesthetically displeasing. Dry cooling towers are cooled by conduction and convection. Warm water is passed through a heat exchanger where air is passed over the coils containing water, cooling it. This is very much like the Figure 5-6 Cooling towers in Didcot Power Station in England. 5 The optimal temperature for plankton, the major source of food for many aquatic ecosystems, varies by only a few degrees. For example, the optimum temperature for growth of green a lgae is 30°C, whereas blue-green algae thrive at about 30-35°C. Thermal discharges therefore favor production of blue-green algae over green algae. Blue-green algae are a poorer source of food and can be toxic to fish. 104 Chapter 5 - Thermal Energy radiators in automobiles. No matter what method of cooling is used, the heat always ends up in the atmosphere. As we shall see, this heat cannot be disposed of and therefore directly contributes to global warming. Example 5-2: Estimate the thermal efficiency of modern power plants using fossil fuels. Solution: A typical, modern steam power plant operates between temperatures of 600oC at the exit of the boiler and 35oC inside the condenser. An ideal (Carnot) plant operating between these two temperatures would have an efficiency of: ηideal = 1 35 + 273 = 65% 600 + 273 Depending on the type of plant, practical plants have efficiencies far lower than this at around 30-40%. This is because much of the energy is used to raise water to high-temperature steam, or lost to friction in turbines and generators. In the case of fossil plants, if losses due to extraction, processing, and transport are included, the overall efficiencies will be much lower in the order of 10-20%. Figure 5-7 shows various losses at different stages of power generation from fossil resources. Cogeneration Cogeneration or CHP (combined heat and power) is the simultaneous production of electricity and heat. In this system, a primary power plant produces electricity, but unlike the simple power plants where exhaust is cooled to atmospheric temperatures, cogeneration utilizes the thermal energy left in the exhaust to drive a second thermodynamic device, which either produces additional power or is used directly for heating applications. Furthermore, some of the steam can be extracted at different pressures for industrial applications or home use. Recent advances in gas turbine technology allow high-temperature combustion of natural gas, which can be used as the primary method of power generation. The exhausts of these turbines are sufficiently hot to be subsequently used in producing additional electricity or heat using conventional steam power plants, resulting in greater conversion efficiencies and lower pollution than the traditional generation methods. The addition of the second turbine boosts combined efficiency to about 60%, which is superior to conventional coal and nuclear power plants with efficiencies of around 33%. When the waste heat is used directly for industrial processes, efficiencies as high as 85% have been found to be possible.6 This technology, generally referred to as the combined cycle combustion turbine (CCCT), has the additional advantage of releasing less heat into the atmosphere, limiting global warming and other environmental damage. The gas turbine operates by using gas (derived 6 M anufacturing Energy Consumption Survey, Energy Information Administration, DoE, 1996 (http://www.eia.doe.gov/emeu/mecs). 105 Underground Resources Extraction Processing Transport Coal Oil Natural Gas 50% 30% 67% Chemical Energy Boiler/Furnace 80-85% Thermal Energy Turbine/Engine 30-45% Mechanical Energy Generator 90-95% Electrical Energy Figure 5-7 Fossil plant energy losses at various points from extraction to power generation. from the gasification of coal or natural gas) as its primary fuel. Natural gas turbines are particularly advantageous over conventional oil and coal plants because there is no emission of sulfur and negligible emission of particulates. Also, NOx emission is cut by 90% and carbon dioxide emission by 60%. Another advantage of this technology is that power can be distributed. This means that small-scale power generation facilities can be constructed using hybrid systems consisting of solar panels, micro-turbines, and wind turbines that can produce enough electricity for small communities such as shopping malls, large office buildings, etc. W hen power is not needed, the excess electricity could be sold to utility companies, reducing their peak loads. We will discuss this issue in greater detail in Chapter 13.7 Question: Explain the limitations inherent in the operation of steam and gas turbine cycles. What is the advantage of a combined cycle over steam and gas turbine cycles operating alone? Answer: Because of material limitations, mainly the hydrogen embrittlement used in piping, the peak temperature of the steam cycles is limited to below 1100°C. The gas turbines, on the other hand, have exhaust at temperatures as high as 450°C, and much of the energy is lost to the atmosphere. The combined cycle takes advantage of the high TL of the gas turbine and the low TH of the steam cycle to achieve a greater efficiency than can be achieved by either when used alone. In this technique, heat is added at a high combustion temperature (topping cycle) and rejected at the relatively low temperature of the condenser or smoke stack (bottoming cycle). Example 5-3: A cogeneration plant uses combined gas turbines and steam power plants. Assuming a total of 200 kg of natural gas is burned every second, what is the plant’s overall efficiency? The gas turbine has a thermal efficiency of 40%, whereas the efficiency of the steam power plant is only 33%. Assume methane has a heating value of 50,000 kJ/kg. A challenge problem for the more mathematically inclined: A cogeneration plant combines a gas turbine with efficiency hGT w ith a steam turbine with efficiency hST. Show the cogeneration plant has a combined efficiency of: hCC = hGT + hST (1 - hGT). What is the overall efficiency of a combined plant if gas turbine and steam turbine efficiencies are 40% and 33% respectively? Compare your answer with the example given in this chapter. 7 106 Chapter 5 - Thermal Energy Solution: The total heat input into gas turbines is equal to the mass flow rate of the fuel multiplied by its heating value 200x50,000 = 10 MWt (megawatts thermal). The power output from the primary cycle (gas turbine) is equal to heat input times the efficiency, 10x0.40 = 4 MWe (megawatts electric), and heat rejected in the exhaust is 10-4 = 6 MWt. In simple cycles, this heat is normally rejected to the atmosphere. In cogeneration cycles, however, we can generate additional electricity by using this heat to drive a second steam turbine. Since the thermal efficiency of steam turbines is only 33%, we have an additional 6x0.33 = 2 MWe (megawatts electric) from this turbine, for a total of 4+2 = 6 MWe from both the primary and secondary systems, and a production of 50% more power by cogeneration. As a result, the overall efficiency of the cogeneration plant has increased to 6 MWe/10 MWt = 60%. Air Conditioners and Refrigerators The second law explains how the Universe is continuously slipping into chaos. This does not mean that there cannot be (on a local scale) a transformation from chaos to order. In fact, this is the main mechanism by which we can defy nature. When we build houses, we change the randomly distributed bricks, lumber, and clay into structured walls of living rooms, bedrooms, and kitchens. We bring order into our house by cleaning it. What the second law precludes us from doing is not creating order, but creating order without causing even more disorder somewhere else (usually in the neighborhood). Air conditioners and refrigerators are devices that move heat away from a space in defiance of the common perception that heat moves from a higher to a lower temperature. The price is of course the expenditure of additional energy in terms of electricity and creation of disorder outside the immediate neighborhood of these devices. The operation of these devices can be best described as the heat engines operating in reverse. Heat is removed from the space (inside the refrigerator or air-conditioned room) and dumped into a second reservoir at a higher temperature. In the case of the household refrigerator, the second reservoir is the kitchen. In the case of the air-conditioner, it is the outside air. Energy input in the form of electricity or heat is needed to make the uphill transfer of heat possible (Figure 5-8). Heat Pumps As explained in the second law, the thermal energy of any substance vanishes only at absolute zero temperature (-273°C). This means even cool outdoor winter air has some thermal energy. The heat pump is a device that utilizes this thermal energy by bringing it into the house and heating its interior. Of course, by removing this heat, we make the 107 Expansion value Evaporator Condenser high pressure low pressure Compressor Figure 5-8 Refrigerator outside temperature even cooler! In order to move this energy inside, a heat pump circulates a fluid called refrigerant which absorbs heat from outdoor air and releases it inside. Heat pumps can be used for cooling as well. This process is the reverse of the heating process; it removes the heat from the space to be cooled and dumps it into the already warm outdoor environment. The operation of a heat pump as a heating device is shown in Figure 5-9a. The refrigerant flows inside a closed loop. At point 1, the refrigerant vapor enters a compressor where it is compressed to a temperature warmer than the indoor air. The compressor needs some energy, usually in the form of electricity, in order to function. At point 2, the heated refrigerant enters an indoor heat exchanger where it gives off its thermal energy and, with the aid of a fan, uniformly heats the room. In the process, some of the vapor is condensed back to liquid (point 3) inside the heat exchanger (thus the name condenser). The liquid is then expanded through a valve or capillary tube at point 4, where it rapidly expands and cools. The mixture then enters a heat exchanger, where the heat from outside air causes it to vaporize (thus the name evaporator). An outside fan facilitates this heat transfer. The refrigerant vapor leaves the evaporator at point 1 and the cycle repeats. During summer, when cooling instead of heating is desired, the direction of flow is reversed (See Figure 5-9b) and the heat exchangers reverse functions. In this mode, the outside heat exchanger is a condenser where heat is extracted, whereas the inside heat exchanger acts as an evaporator, removing heat from the space where cooling is desired. The performance of heat pumps is defined in terms of the amount of heating or cooling that is achieved per amount of work energy (electricity) that is needed to run the compressor. This is called the coefficient of performance (COP). The COP for practical heat pumps is around 4-5, meaning heat pumps can provide four to five times more heating or cooling than electricity consumed. In comparison, electric heaters have efficiencies close to 100%, oil and gas heaters have efficiencies of 50% to 90%, and wood stoves’ heating efficiencies range from 20% to 60%. The COP decreases markedly once outside temperatures fall below around −5 or −10 °C. In the United States, it is customary to specify the performance of a heat pump by two numbers, the COP as defined above for heating, and the Energy Efficiency Ratio (EER) for cooling. The EER is expressed in Btu/ Wh, and is the ratio of cooling capacity given in Btu/h to required electrical power in watts.8 For large commercial units, chillers are rated in kilowatts per ton. Because each ton of refrigeration is equal to 12,000 Btu, we have 8 (a) (b) Figure 5-9 Heat pumps a) heating cycle; b) cooling cycle R emember that Btu is the US unit of energy, while Wh is the unit of energy in SI systems of units. So much for our creativity! 108 Chapter 5 - Thermal Energy Energy Boosters Mathematical Interlude ... I n line with the definition proposed for thermal efficiency of heat engines for refrigerators and heat pumps, it is most convenient to define efficiency in terms of the desired effect (cooling or heating) as compared to the work that is necessary to achieve this effect. For a Carnot heat pump and refrigerator, the following results are obtained: COP ideal, HP = COP ideal, R = TH TH - TL TL TH - TL (i) (ii) TL and TH are temperatures of cold and hot reservoirs and must be expressed in the Kelvin scale. Of course, construction of such devices is not practical because there are always friction and conduction losses that cannot be completely eliminated. Example: A heat pump is to be used to heat a house during the winter to 20oC (293 K). The house loses heat at a rate of 100,000 kJ/h when the outside temperature drops to -8oC (265 K). What is the minimum power required to drive this heat pump? Solution: Minimum power usage can be achieved when the heat pump works reversibly as a Carnot heat pump. The COP of this heat pump would be: COP = 293/(293-265) = 10.5. That means for each unit of power consumed, 10.5 units of heat can be supplied to the room. The power input to the compressor is then 100,000/10.5 = 9556 kJ/h (or 2.7 kW). If the house was going to be heated by an electric resistance heater instead, we would have needed 10.5x2.7 = 28.35 kW of electric power. This example shows that by investing a small amount of work in a heat pump we can supply a great amount of heat. For this reason, heat pumps can be appropriately called “energy boosters”. EER = 3.413 x COP kW/ton = 12 EER (5-2) (5-3) Summary Understanding laws of thermodynamics is fundamental to understanding the workings of the universe. In this chapter we covered these laws and their relevance in designing useful thermal devices. In describing the working principle of such devices (a thermal power plant, a heat engine, a refrigerator, or any other thermodynamic system for that matter) we concluded that: 1) At least two reservoirs, one at a high temperature and the other at a low temperature, are needed. This is one of the important consequences of the second law of thermodynamics, which states that we cannot convert heat to work with a single heat source. In the case of a steam power plant, the steam generator and condenser are the two reservoirs. In internal combustion engines, the two heat reservoirs are hot combustion gases and cold exhaust gases. 2) Some form of energy is always needed to provide heat to the high-temperature heat reservoir. For power plants, energy needed to heat water comes from an external source 109 which could be fossil, nuclear, or less commonly solar or geothermal. 3) To increase efficiency, we must either increase the temperature of the source or lower the temperature of the sink. We are limited to atmospheric temperatures for the sink, but we can increase the source temperature. In power plants, we can raise steam temperature by increasing the boiler pressure (water boils at a higher temperature if the pressure is greater). Raising the compression ratio, minimizing heat losses, and using better fuels can similarly increase internal combustion efficiency. 4) Higher efficiencies not only reduce fuel consumption, but also protect our environment by producing fewer pollutants. In addition, higher efficiency means a smaller fraction of energy must be disposed of as waste heat, commonly termed “thermal pollution,” which is a major source of global warming. Additional Information Books 1. El-Sayed, Y., The Thermodynamics of Energy Conversions, Elsevier Direct Science, 2003. 2. Cengel, Y. A., Heat Transfer: A Practical Approach, McGraw-Hill, Inc., 1998. 3. Rifkin, J., Entropy, The Viking Press, 1980. 4. El-Wakil, M/ M., Power Plant Technology, McGraw-Hill, Inc., 1984. Periodicals 1. Energy and Buildings, Science Direct Elsevier Publishing Company. An international journal publishing articles about energy use in buildings and indoor environment quality. 2. Energy Conversion and Management, Science Direct Elsevier Publishing Company. This journal focuses on energy efficiency and management; heat pipes; space and terrestrial power systems; hydrogen production and storage; renewable energy; nuclear power; fuel cells and advanced batteries. 3. Energy and Buildings, Science Direct Elsevier Publishing Company, An international journal dedicated to investigations of energy use and efficiency in buildings. Government Agencies and Websites 1. How Things Work (http://howthingswork.virginia.edu). 2. How Stuff Works (http://www.howstuffworks.com). 3. California Energy Commission Consumer Energy Center (http:// www.consumerenergycenter.org). 110 Chapter 5 - Thermal Energy Exercises I. Essay Questions: 1. What is heat and its relation to temperature? How did the concept of heat change throughout the centuries? 2. The temperature of the water at the bottom of Niagara Falls is slightly warmer than the water at the top of the waterfall. To what do you attribute this temperature difference? 3. The highest temperature ever recorded in Death Valley, CA is 54.7 °C. What is the temperature in degrees Fahrenheit? 4. Define heat capacity, specific heat, and thermal conductivity. Does a substance with a high specific heat necessarily have a high heat capacity and thermal conductivity? 5. Which one is colder during the winter, an iron railing or a wooden fence post? 6. A wooden pan heated to 80oC can be picked up comfortably, but a similar pan made of copper can burn your hand. Why is this? 7. What are the three modes of heat transfer? Under what conditions do any of the modes become more significant? 8. Why do many frying pans have wooden handles? 9. Name the main components of a steam power plant and their functions. 10. Name the main components of a gas turbine, a heat engine, and a power plant. Explain their functions. 11. Name the main components of an air conditioning system and their functions. 12. What are the differences between an air conditioner and a heat pump? 13. As a car is coming to a stop, its kinetic energy continuously decreases. What happened to this energy? 14. Why would one use heat pumps when a heating coil will also do the job? 15. An inventor claims to have designed an engine that has eliminated nearly all frictional losses and uses insulating material with relatively little heat losses; the efficiency of this engine is therefore very close to unity. How do you evaluate this inventor’s claims? 16. For each of the following devices, describe basic operation, typical efficiency, and the working fluid. In each case, explain what constitutes the source and the sink: a. Internal combustion engine b. Steam power plant c. Jet aircraft engine d. Refrigerator 17. Which of the following situations is allowed by the second law of thermodynamics? a. Designing a heat engine that exploits the temperature differences in the top and bottom of the oceans b. Converting 100 joules of heat energy into 100 joules of work c. Converting 100 joules of work into 100 joules of heat energy d. Removing heat from cold outside air to heat inside of a house in winter e. Reducing the waste heat from a power plant to zero with super insulating materials 18. Which of the following violate the second law of thermodynamics? Explain. a. You visit a friend’s house and find it to be tidier than you found it in your previous visit. b. Spraying water on the pavement cools the air. c. A glass is dropped on a hard surface but does not break. d. A glass is dropped on a hard surface and shatters into many small pieces. e. A coin lands head up ten times in a row. f. You run a film backward to see a scene you missed. 111 19. The energy conversion efficiencies in a 3 step process are 60% for the first step, 40% for the second, and 80% for the third. What is the overall efficiency for this three-step process? 20. Thermal images of an airplane and an automobile are shown in pictures below. Explain what the different colors mean. Can you identify the hottest regions of these objects in these images? (Images courtesy of Thermotronics Inc, Brazil) O substance increases, but their kinetic energy does not d. Both potential and kinetic energies of the molecules of the substance increase e. None of the above 4. A BTU is a unit of a. Energy b. Power c. Heat flow rate d. Specific energy e. None of the above 5. Heat transfer in solids is mostly by a. Conduction b. Convection c. Radiation d. Conduction and convection, but not radiation e. Conduction, convection and radiation 6. Heat transfer in liquids is mostly by a. Conduction b. Convection c. Radiation d. Conduction and convection, but not radiation e. Conduction, convection and radiation 7. Heat transfer in flames is mostly by a. Conduction b. Convection c. Radiation d. Conduction and convection e. Convection and radiation 8. The heat transferred by conduction increases with a. The temperature gradient across the object b. The thermal resistance across the object c. The thickness of the object d. The volume of the object e. All of the above 9. Which of these statements is correct? a. Conduction is the transfer of heat by molecular interaction. b. Convection is the transfer of heat by bulk motion. c. Radiation is the transfer of heat by electro- 55 50 45 40 35 30 25 20 C o 30 25 20 15 10 C II. Multiple Choice Questions 1. Thermal energy results from the motion of a. Electrons b. Nuclei c. Molecules d. Mass e. All of the above 2. Heat is a. A substance with mass that flows from a high temperature toward a low temperature b. A mass-less substance that flows from a high temperature toward a low temperature c. The result of kinetic motion of particles d. Equal to the work required to run a heat engine e. The same as temperature 3. As a substance is heated a. Mass decreases because some of it goes into heat b. Mass increases because heat is added c. Potential energy of the molecules of the 112 Chapter 5 - Thermal Energy magnetic radiation. d. All of the above. e. None of the above. 10. The materials listed in order of increasing thermal conductivity are a. Diamond, water, and air b. Air, water, and copper c. Aluminum, hydrogen, and vacuum d. Copper, water, and air e. Ice, Styrofoam, and silver 11. Radiant energy (light) travels a. In a medium, but not in vacuum b. In gases, but not in liquids and solids c. In both a vacuum and a medium d. Faster in a medium than in a vacuum e. With infinite speed in a vacuum 12. Radiant energy (light) travels a. A straight line b. In waves c. In either a straight line or in waves d. Faster in a medium than in a vacuum e. With infinite speed in a vacuum 13. Night vision cameras operate in the a. UV range b. X-ray range c. Visible range d. Infrared range e. TV range 14. The reason sand gets warmer than water at sunny beaches is that a. Sand is denser than water b. Sand can trap heat much better than water c. Sand has a higher specific heat than water d. Sand has a lower specific heat than water e. Sand is less transparent than water to solar energy 15. Why do most apples appear red to us? a. Red apples absorb the red portion of visible light. b. Red apples transmit the red portion of visible light. c. Red apples absorb all colors except red. d. Red apples absorb the infrared portion of visible light. e. Red apples reflect the ultraviolet portion of visible light. 16. A lamp which has an efficiency of 15% a. Converts 15% of thermal energy to light b. Converts 15% of electrical power to light c. Converts 15% of electrical power to light and heat d. Converts 85% of electrical power to light e. Uses only 15% of the incoming electrical power to work 17. A glass cup falls from edge of a table. The potential energy of the glass cup a. Converts to heat only b. Converts to heat and sound c. Converts to sound only d. Converts to static charge e. Converts to sound and electricity 18. When you stir a hot cup of coffee with a metal spoon, the coffee a. Warms mainly by conduction through the spoon b. Warms mainly by convection c. Cools mainly by conduction through the spoon d. Cools mainly by convection e. Stirring does not affect its temperature 19. A battery is a convenient device to convert a. Electrical energy to mechanical energy b. Chemical energy to thermal energy c. Thermal energy to electrical energy d. Chemical energy to electrical energy e. Thermal energy to chemical energy 20. During photosynthesis a. Light is converted to chemical energy b. Light is converted to electrical energy c. Light is converted to thermal energy d. Thermal energy is converted to light e. Thermal energy is converted to mechanical energy 113 21. According to the first law of thermo- dynamics, a. Energy cannot be created, nor can it be destroyed b. The available energy of a system in all real processes decreases c. Work can be converted entirely to heat d. Heat cannot be converted entirely to work e. All of the above 22 Entropy a. Increases for all real processes b. Decreases for all real processes c. Is a measure of disorder in the system d. Remains constant if energy remains constant e. Both a and c 23. Matter resources are depleted by being ________, whereas energy resources are depleted by being _________. a. Dispersed, destroyed b. Consumed, lost c. Dispersed, transformed d. Destroyed, consumed e. Lost, dispersed 24. According to the second law of thermodynamics, a. One day the universe will reach a heat death b. One day we can invent devices to go back in time c. One day we can convert frictional losses completely back to work d. One day we can design refrigerators that do not require any work input e. One day all the processes cited above will be possible 25. According to the second law of thermodynamics, a. Some energy is lost when it transforms from one form to another b. Energy can be neither created nor destroyed c. Energy becomes more dispersed during any real process d. Entropy increases for all real processes e. All of the above 26. Efficiency of real heat engines can be shown to be equal to 114 Tc Th T b. 1 - h Tc a. 1 c. 1 d. 1 Qc Qh Qh Qc Q e. 1 - h Wnet 27. Thermal efficiency of a heat engine is a number between a. 0 and 1 b. 0 and 100 c. 0 and ∞ d. - 1 and +1 e. - ∞ and +∞ 28. Coefficient of performance of a refrigerator is a number between a. 0 and 1 b. 0 and 100 c. 0 and ∞ d. - 1 and +1 e. - ∞ and + ∞ 29. The efficiency of car engines can be improved if a. We design a heat sink that operates at a lower temperature b. We use better fuels c. We reduce friction d. We increase the compression ratios e. All of the above 30. The temperature of a healthy body can be expressed in different systems of units as a. 37 oC, 98.6 oF, and 310 K b. 100 oC, 212 oF, and 373 K c. 37 oC, 98.6 oF, and 37 K d. 37 oC, 98.6 oF, and 497 K e. 37 oF, 98.6 oF, and 310 K 31. To make fusion reactions possible, the gaseous mixture of deuterium and tritium must be heated Chapter 5 - Thermal Energy to 100 million degrees Celsius. This temperature is roughly equivalent to ____________ degrees Fahrenheit. a. 55 million b. 100 million c. 180 million d. 212 million d. None of the above 32. According to the zeroth law of thermodynamics, a. Temperatures lower than zero absolute temperature can never be achieved b. The total energy of a substance will always remain the same c. Objects at equilibrium must have the same temperatures d. Heat always flows in the direction of decreasing temperature e. There is no such law 33. The “efficiency” of an electric heater is defined as the ratio of the a. Heat energy produced to the electrical input b. Output voltage of the heating element to the voltage of power supply c. Electrical energy into the heater to the thermal energy out of the heater d. Light output to the electrical energy input e. Heat energy produced to heat energy used to produce the electricity 34. Which of the following observations are consistent with the second law of thermodynamics? a. Aging is a natural process. b. Earthquakes tend to cause destruction. c. Heat flows from higher to lower temperatures. d. Some information is always lost through transmission. e. All of the above. 35. Which of the following observations are consistent with the second law of thermodynamics? a. If you puncture a hole in an inflated helium balloon, helium will flow out. b. The ultimate fate of the universe is a heat death where temperature, electric potential, pressure, etc. are uniform. c. We can never build a thermal engine with 100% efficiency. d. Even the cooling of a room is associated with the entropy increase of the entire universe. e. All of the above. 36. Which of the following observations is/are consistent with the first law of thermodynamics? a. Aging is a natural process. b. Energy is neither created nor destroyed. c. Heat engines can only reach efficiency of unity if there are no frictional losses. d. Two objects at the same temperature as a third object are themselves at the same temperature. e. All of the above. 37. Which of the following observations are consistent with the first law of thermodynamics? a. When we turn on a light bulb, some energy is lost as heat. b. A light bulb is a device that converts electrical energy into light and heat. c. In a bicycle, some mechanical energy is transformed into another form of mechanical energy. d. In a nuclear reaction, some mass is converted to energy. e. All of the above. 38. The four basic components of a thermal power plant cycle are a. Pump, compressor, turbine, and condenser b. Pump, turbine, boiler, and cooling tower c. Pump, boiler, turbine, and condenser d. Steam, water, river, and fossil fuels e. Heat, work, energy, and entropy 39. Saving one BTU of electric energy a. Conserves zero BTU of total energy b. Conserves less than one BTU of total energy c. Conserves one BTU of total energy d. Conserves about 3-4 BTUs of total energy e. Has no relationship to saving other forms of energy 40. Refrigerators a. Operate in violation of the zeroth law of 115 b. c. d. e. thermodynamics Operate in violation of the first law of thermodynamics Operate in violation of the second law of thermodynamics Operate in violation of the third law of thermodynamics Do not violate any laws of thermodynamics c. Jet engines d. Solid-fuel rockets e. Both c and d III. True or False? 1. Heat is a mass-less substance that resides inside an object. 2. Temperature is a property of the material from which an object is made and represents the amount of heat that is contained in that object. 3. Different objects will eventually reach the same temperature when they remain in contact for a long time. 4. Heat is energy transferred from an object at high temperature to another at low temperature. 5. Heat is the total amount of energy in an object. 6. Energy is conserved, but only if no friction is present. 7. Energy can be converted from one form to another. 8. Heat can be entirely converted to work and vice versa. 9. Heat can never flow from a low to a high temperature. 10. Specific heat is a measure of the amount of energy a substance can store. 11. The absolute best insulator is a vacuum as there are no molecules to pass on energy. 12. There is no limit to how much an object can cool. 13. There is no limit to how much an object can warm. 14. An ideal heat engine that works with no friction is 100% efficient. 15. The only known phenomenon that seems to violate 41. If you leave your refrigerator door open, the average temperature in the room will be a. Lower than it was before b. Higher than it was before c. The same as it was before with uniform temperature throughout the room d. The same as it was before, but some regions will be hotter and others will be colder 42. Roughly, what percentage of energy from burning coal is converted to electricity? a. 10-20% b. 30-40% c. 50-60% d. 70-80% e. 90-100% 43. Jet engines a. Are reaction-type heat engines b. Require oxygen or air to operate c. Cannot operate in space because there is little or no oxygen d. Are cleaner to operate than gasoline engines, because they function under leaner conditions e. All of the above 44. Which of the following is not considered an internal combustion engine? a. Diesels using synthetic biofuels b. Gasoline engines c. Gas turbines d. Steam turbines e. All are internal combustion engines 45. Which of the following is not considered an external combustion engine? a. Stirling engines b. Steam engines 116 Chapter 5 - Thermal Energy the second law of thermodynamics is a hurricane. 16. A transformer is a device to convert one form of electrical energy to another. 17. In a bicycle, one form of mechanical energy converts to another form of mechanical energy. 18. According to the second law of thermo-dynamics, nature always prefers order over disorder. 19. Since time always proceeds from past to present to future, running a film backward is in violation of the second law of thermodynamics. 20. Work, heat, and energy have the same units. 21. Work, heat and energy are identical in every sense. 22. Work is a higher quality form of energy than heat. 23. Solar energy is of a higher quality form of energy than fossil fuels. 24. Heat engines can be made close to 100% efficient if we find better materials and eliminate all frictional losses. 25. The construction of a time machine, although theoretically possible, will not be technically feasible for a very long time. IV. Fill-in the Blanks 1. Based on the assumption of caloric theory, heat is a ________ called “caloric”. 2. When burned, approximately ______ percent of gasoline energy ends up in the exhaust pipe. 3. Radiation coming from the nuclei of atoms is called __________ rays. 4. Heat engines are devices in which thermal energy is converted to _________. 5. No heat engine can operate with only one heat ___________. 6. It is impossible to construct a heat engine which has the efficiency of unity, unless it operates in an atmosphere at _____________ temperature. 7. The ratio of energy delivered to energy used is called the ____________ efficiency. 8. Combined cycle combustion turbine uses the high temperature exhaust of the gas turbines to achieve a greater __________. 9. Heat pumps usually have ________ greater than one. 10. According to the _____ law of thermodynamics, temperature of zero kelvin can never be attained. V. Project I - Energy balance In this project you are asked to estimate your total daily energy consumption. 1. Make a table showing your daily food intake and the total food calories you consume. Convert this energy to joules. 2. Make a table showing all the electrical appliances you routinely use (electric oven, refrigerator, heater, stereo, lights, hair dryer, etc.) Estimate the number of hours you use each device. Multiply time by the power consumption (wattage) to calculate the total energy consumption in kilowatt-hours. If there is more than one person in your household, correct the result by dividing this number by the number of people sharing each device. 3. Assuming electricity was produced in a power plant with efficiency of 33%, how much thermal energy was needed to meet your electric power requirement. 4. Estimate total energy requirement for all the gas appliances in your house. 5. Estimate the total energy required for your transportation need. This can be done by dividing your daily travel in miles by the gas mileage your car gives (in mpg) and multiplying the results by energy content in one gallon of fuel. 6. Add items 1-5 to estimate your total daily energy consumption. 117 Project II - Gas vs. electricity In this project you are asked to examine the electric and gas bills for your home for a month. Find a copy of your gas and electricity bills (if you don’t get one, use those from your parents or a friend) and write down: 1. The amount of electricity used in kilowatt-hours. 2. The amount of gas used (in the United States this is usually given in therms, which is equal to 100,000 BTU). 3. The lowest, highest, and average prices charged during that month. Note that prices may vary depending on the month, time of the day and during peak hours. 4. Total amount of energy consumption (thermal and electrical) in megajoules and kilowatt-hours. 5. The average power consumed by you in kilowatts (Divide the total energy used by the number of hours in the month). 6. Determine average cost of electricity in $/kWh and $/MJ (1 kWh = 3.6x106 J). 7. Determine average cost of gas in $/therm and $/ MJ. 8. Which one (electricity or natural gas) costs more and why? Is the price differential justified? Explain. 9. How much do you save (lose) if you switch to allelectric appliances? 118