Chapter 16: The Zeroth and First Laws - Thermodynamics Paper PDF

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Okay, here is the structured markdown format of the text from the images you sent. I have tried to maintain all the information, equations and formatting as faithfully as possible: ### 168 THE ZEROTH AND FIRST LAWS #### 16.1 Introduction So far you have studied two forms of energy-mechanical and thermal. Mechanical energy is a property of tangible objects. Two types of mechanical energy are potential energy and kinetic energy. Potential energy, one result of work, can be changed to kinetic energy-energy of motion. A motionless ball poised at the top of an inclined plane has potential energy. As the ball rolls down the inclined plane, it gains kinetic energy as it loses potential energy. When the ball reaches the bottom of the plane, the last of its gravitational potential energy disappears and it rolls along the flat surface with only kinetic energy. Total mechanical energy (E) is the sum of the kinetic and potential energies due to the motion and position of physical objects. Once the appropriate reference points for determining the system's motion and position are established, the system's total mechanical energy can be known. Subsequently, only the changes of the system's total mechanical energy ($\Delta E$) are important from a physics perspective. Thermal energy is due to the rapid, random motion of the molecular, atomic, and subatomic particles of matter. Like mechanical energy, thermal energy can be subdivided into potential energy and kinetic energy. The particles of a substance are constantly moving; therefore, they have kinetic energy. Their average kinetic energy is proportional to the temperature of the substance. **16-2** Mechanical potential energy can change to mechanical kinetic energy. #### 16.2 The Zeroth Law of Thermodynamics Some materials conduct heat well, while other materials are good insulators. An ideal insulating wall through which no thermal energy can pass is called an adiabatic boundary. An ideal conductor of thermal energy is called a diathermic material. Although no completely adiabatic or diathermic materials exist, the concepts are useful for simplifying discussions. As you have probably noticed, when you place a hot object in contact with a cold object, the cold object becomes hotter, and the hot object becomes cooler. In time, the two objects reach the same temperature. That is, they reach a state of thermal equilibrium. Thermal energy has flowed from the hot object to the cold object. As you learned in Chapter 15, the flow of thermal energy is called heat. The image depicts what is called the zeroth law of thermodynamics. This law states that two systems that are in thermal equilibrium with a third system must be in thermal equilibrium with each other. The law received its name because it is more basic than either the first or second law but was formulated after the other laws already had been named. In (a), system A is separated from system B by an adiabatic barrier, and both are linked to system C by diathermic barriers. Although A and B cannot exchange thermal energy with each other, both can exchange thermal energy with C. In (b) the barriers have been switched so that A and B can exchange thermal energy with each other, but C is thermally insulated from both A and B. According to the zeroth law, if no net energy exchange occurs in (a), then none will occur in (b). The principle becomes still more understandable when you view it in terms of temperature. In (a), systems A and B are at the same temperature as C. (You must, of course, assume that each system is itself at a uniform temperature.) System A must therefore be at the same temperature as system B. When the adiabatic barrier between them is replaced with a diathermic barrier, neither system will warm (that is , transfer thermal energy to) the other. Moreover, since all three systems are at the same temperature, no thermal energy can flow in any direction, regardless of how the barriers are placed. #### 16.3 The General Law of Conservation of Energy- The First Law Before progressing further, we need to gather together what we know about energy transfers in order to establish a fundamental or general energy conservation principle. Energy can be added to a system by either of two processes: (a) mechanical work ($W_{net}$) through the application of external nonconservative forces or (b) heat transfer (Q) through temperature differences with the system's surroundings. The energy transferred to the system by these means is seen as a change of the internal energy of the system ($\Delta U$) or as a change in the system's total mechanical energy ($\Delta E$) or both. The general energy conservation law can be written as $Q+W_{net} = \Delta U + \Delta E$ **(16.1)** When we discussed basic mechanics, we assumed that no heat transfers took place and no changes of internal energy occurred ($\Delta U = 0 J$). When discussing basic thermodynamics principles, we will make the assumption that the total mechanical energy of the system is constant ($\Delta E$ = 0 J). Therefore, the only forces doing work on the system are nonconservative forces. Equation 16.1 can then be rewritten as $Q+W_{net} = \Delta U $ **(16.2)** Rather than being concerned about the work done on a system, as we were in our study of mechanics, it is more useful in thermodynamics to evaluate the effects of a system on its surroundings; therefore the work notation in Equation 16.2 needs to be modified slightly. Recall from our study of Newton's laws that every force on a system is paired with an opposite force acting on another system. It follows that if a system's surroundings do mechanical work on it through the application of a onconservative force, then the system must also do work on its surroundings via the reaction force. The work by the system on its surroundings is therefore the negative of the work on the system ($W_{net} = -W$). Equation 16.2 then becomes: $Q - W = \Delta U$, or $Q = \Delta U + W$ **(16.3)** Equation 16.3 is the mathematical statement of the first law of thermodynamics. The first law extends the principle of the conservation of total mechanical energy to internal energy as well. We will investigate the applications and limitations of the first law in the following discussion of thermodynamic processes. #### 16.4 Heat Engines Thermal energy can be changed into mechanical energy. An engine called a heat engine can do mechanical work by absorbing and discharging heat. The simplest "machine" that converts thermal energy to work is an expanding gas. For a gas to expand usefully, it must be confined in an expandable container. One such container is a cylinder fitted with a gas-tight piston. Assuming that the piston is massless and frictionless simplifies calculations. As the gas expands, it is no longer in thermal equilibrium. It heats or cools unevenly. To avoid this problem, we allow the gas to expand in extremely minute steps, letting it return to thermal equilibrium between steps. Consequently, the gas expands without ever being far from thermal equilibrium. A process that proceeds in this way is called a quasi-static process. For quasi-static processes, the gas pressure inside the cylinder is at all times in equilibrium with the external pressure. When the gas is compressed from a volume $V_1$ to a volume $V_2$ by an external pressure $P$, work is done on the gas. (You can verify that energy is added to the gas because it warms when it is compressed.) The simplified formula for work is: $W = Fd$ **(16.4)** Pressure is force per unit area, so force exerted by the gas equals pressure times the cross-sectional area of the piston: $F = P_{gas}A$ Substituting for force in Equation 16.4, $W = (P_{gas}A)d$. 22. Thermodynamics concerns the work done on the system more than the work the system does on its surroundings. 23. The work done during a thermodynamic process graphed on a P-V diagram does not depend on the path the process takes. 24. A steaming cup of coffee on a tabletop is an open system. 25. Pushing down on the plunger of a tire air pump causes the air in the pump to undergo an isochoric process. 26. Engines that heat the working fluid only once and then discharge it have low efficiencies compared to those that heat the working fluid over and over again. 27. James Watt invented the first practical steam-poweredengine. 28. A Carnot engine is more efficient if the temperature difference between the hot and cold reservoirs is increased. 29. A heat engine would be 100% efficient if it discharged no heat to the cold reservoir. 30. Entropy is a form of energy. 31. As with some other state variables, it is simpler to determine the change of entropy than to measure it at a given state. 32. The fact that your bedroom gets messier with time is an example of the second law of thermodynamics inaction. **033.** A pressure of 1.52 x $10^5$ Pa forces a gas to compress from a volume of 5.00 x $10^{-3} m^3$ to a volume of 2.50 x $10^{-3} m^3$. How much work is done on the gas, in Nm? **034.** A gas in a cylinder with a cross-sectional area of 60.0 $cm^2$ holds the piston at a height of 5.00 cm when a force of 18.0 N is applied. Then, under the same force, the gas expands in a quasi-static process to a height of 7.50 cm. a. What is the gas's original volume, in $m^3$? b. What is the original pressure on the gas in N/$m^2$(Pa)? c. What is the final volume of the gas, in $m^3$? d. How much work does the gas do, in J? **035.** A gas expands as Figure (a) shows. a. How much work does the system do in step 1? b. How much work does it do in step 2? c. How much work does it do overall? The image contained a graph. The X axis is Volume, V($m^3$) and the labels are as follows: 1.0, 2.0, 3.0, 4.0, 5.0 The Y axis is Pressure, P (x $10^5$ Pa) and the labels are as follows: 1.0, 2.0, 3.0, 4.0, 5.0 There are two steps labeled 1 and 2. Step 1 is a constant vertical line from Pressure 3.0 down to Pressure 1.0 at Volume 2.0. Step 2 is a constant horizontal line from Volume 2.0 to Volume 5.0 at Pressure 1.0. **037.** A Carnot engine has a hot reservoir at a temperature of 490 K and a cold reservoir at a temperature of 290 K. What is its efficiency? **038.** If the hot reservoir of a Carnot engine is at room temperature (24 °C), what must be the temperature of the cold reservoir in Celsius for the engine to have an efficiency of 50%? **039.** If a ship's steam propulsion boilers produce 1.20 MW of thermal energy at full power, and the propulsion plant is 15% efficient, how much power is discharged to the sea via the seawater cooling system? **040.** A gas expands and contracts in the cycle shown in Figure (c). How much work does each part of the cycle do? * The image contained a graph. The X axis is Volume, V(L) and the labels are as follows: 0, 1, 2, 3, 4, 5 * The Y axis is Pressure, P (x $10^5$ Pa) and the labels are as follows: 0, 1, 2, 3, 4, 5 * There is a cycle indicated with a nearly circular line intersecting the X axis at Volume 1 and Volume 5, and intersecting the Y axis between Pressure 2 and 4. **036.** Find the work done by a gas following one cycle as shown in Figure (b) for a. each step. b. the entire cycle. The image contained a graph. The graph is a closed trapezoid. The X axis is Volume, V(L) and the labels are as follows: 10, 20, 30, 40, 50 The Y axis is Pressure, P (x $10^5$ Pa) and the labels are as follows: 10, 20, 30, 40, 50 The area marked 1 is a vertical line going from points Pressure 50 and Volume 10, to Pressure to 10 and Volume 10. The area marked 2 is a horizontal line going from points Pressure 10 and Volume 10, to Pressure 10 and Volume 40. The area marked 3 is a vertical line going from points Pressure 10 and Volume 40, to Pressure 50 and Volume 40. The area marked 4 is a diagonal line going from points Pressure 50 and Volume 10, to Pressure 50 and Volume 40. **DS041.** Do research and write a brief paper discussing how air conditioning has changed American culture. Include in your discussion an assessment of the net benefits as positive or negative. How important is or should be anticipating the cultural consequences of new technology during the development of that technology? ### Review Questions 1. What thermodynamic state variable is dependent on the temperature of the system? 2. What is the zeroth law of thermodynamics? 3. Discuss the two ways that energy can be exchanged between a system and its surroundings. 4. State the first law of thermodynamics. What principle of mechanics does it extend? 5. Define heat engine. Give an example. 6. Describe the three kinds of thermodynamic systems and give an example of each. 7. Classify each of the following systems as open, closed, or isolated. a. flour in a sifter b. ice cube in an adiabatic calorimeter c. a living human being d. hot coffee in a mug in a cold room e. a leakproof steam engine 8. Why does a heat engine require a fluid to operate? 9. What advantage did the Newcomen engine have over the Savery engine? 10. As a heat engine completes a cycle, how does its final internal energy compare to its starting internal energy? 11. Discuss two ways to thermodynamically (rather than mechanically) improve the efficiency of a Carnot heat engine. 12. What law gives the reason that a heat engine cannot be 100% efficient? 13. Which of the following is not a statement of the second law? a. Thermal energy can flow from cold to hot if work is done. b. Thermal energy cannot be converted entirely to work in a cyclic process. c. The entropy of an isolated system tends to decrease. d. Every natural process directly or indirectly makes the universe more disorderly. 14. How does the theory of evolution contradict the second law of thermodynamics? 15. Discuss several examples which illustrate that it is necessary to do work on a system in order to prevent an increase of entropy. 16. Discuss why the heat death of the universe will not occur. **True or False (17-32)** 17. Mechanical kinetic and potential energies are properties of the macroscopic system, but internal energy is a property arising from the microscopic particles of the system. 18. The zeroth law of thermodynamics establishes the "transitive property of thermal equilibrium"—if A and B are both in thermal equilibrium with C, then they are in equilibrium with each other. 19. Fiberglass insulation approximates a good diathermic material. 20. In order to simplify the statement of the first law of thermodynamics, it is assumed that the total mechanical energy of the system does not change during a thermodynamic process. 21. A quasi-static process proceeds smoothly without any steps or stops. expands in a quasi-static process to a height of 7.50 cm. a. What is the gas's original volume, in $m^3$? b. What is the original pressure on the gas in N/$m^2$ (Pa)? c. What is the final volume of the gas, in $m^3$? d. How much work does the gas do, in J? 22. A gas expands as Figure (a) shows. a. How much work does the system do in step 1? b. How much work does it do in step 2? c. How much work does it do overall? ###### 16C Section Review 1. What property of a system does entropy describe? 2. According to the second law of thermodynamics, what happens to the entropy of a system subject to natural processes? 3. A mixture of ice and water is contained in a near-perfect adiabatic container. As the entropy of the melting ice increases, what must happen to the entropy of the water surrounding it? 4. Briefly discuss how the free expansion of a gas in an adiabatic container increases the entropy of the gas. 5. a. What would be the likelihood of all the oxygen in your classroom clumping together in a 1 L volume in one corner? b. If it did, would the entropy of the gas be higher or lower than is normally the case? 6. The belief that matter is eternal is often a tenet of what system of philosophy? 7. As one follows the progress of total entropy in the expanding universe after the supposed big bang, what direct violation of the second law of thermodynamics must have occurred for the universe to have acquired its present form? 8. What is the flaw in some evolutionists' logic when they appeal to the statistical nature of entropy over immense periods of time as a justification for evolution? ###### 16.15 What Is Entropy? We have already discussed three statements of the second law of thermodynamics. A fourth statement of the second law is that entropy increases in all natural processes. Entropy (S) is another state variable of a system, like volume, temperature, or pressure. Because entropy is related to the microscopic properties of the particles of a system, it is similar in some ways to internal energy. Just as with internal energy, the change of entropy ($\Delta S$) is more important and more easily determined ###### 16.16 Conservation and Degeneration in Nature You may wonder why the universe still has energy available for work if the second law is true. The answer is that God created the universe with an immense supply of usable energy. Obviously, the laws of thermodynamics were not valid during Creation. The first law is a result of the fact that only God can create or destroy. The only exceptions to this law are divine actions. Since the universe began with relatively little entropy, it will be a long time before it reaches a state of maximum entropy. The first law says that energy and mass are conserved. If something is to be conserved, it must exist. Some scientists believe that the physical laws we know now have always been in effect. This belief is consistent with uniformitarianism. Uniformitarian scientists must believe either that matter does not now exist or that it has always existed. Many uniformitarians believe that matter is eternal. Some believe that before this universe was formed, matter existed in the form of subatomic particles. These particles eventually became compacted and then exploded (the so-called big bang). With the energy from the explosion, the particles united to form atoms. Eventually, the early universe developed to its present state. The big bang is only one of the theories of naturalistic evolutionary cosmology. The first law, by itself, neither supports nor refutes this theory of evolution. However, assuming that the primordial universe, highly compacted and ordered, exploded and expanded in an irreversible process, the universe's entropy would have had to rapidly increase during the early period of its supposed expansion. Furthermore, in order for galaxies, stars, and planets to form, a decrease of entropy is required. Scientists have never been able to identify any natural ordering process that would tend to gather particles of dust together into these celestial structures. Such an ordering process could be accomplished only through an intelligent infusion of energy. Therefore, naturalistic evolutionary cosmology is thermodynamically impossible. Evolutionists point out that, according to kinetic theory, the second law is based on probability. Although unlikely, they say, a violation of the second law is possible. Given enough time ten billion years or so a violation is almost inevitable. It is true that the kinetic theory suggests that an entropy decrease is possible. However, there are two reasons that evolutionists are in error when they say that the second law allows evolution. First, no violation of the second law has ever been observed. The second law is based on observations. Until a violation of it is observed, the idea that such a violation can occur is only an idea. Second, the theory of evolution requires not one decrease in entropy but almost continual decreases in entropy, whose effects are preserved by the system. If the second law can be ignored as many times as evolution requires, it is not an accurate reflection of nature. Evolution implies that there is a tendency for a system to become more ordered, but the second law says that the tendency is for a system to become more disordered. The theory of evolution directly contradicts the second law. The second law states that energy is becoming less available for use. Eventu- ally, if the universe is left to itself, all energy will be unavailable for use. The universe will be at a uniform low temperature. Nothing will be able to live. This effect is called the heat death of the universe. This hypothetical heat death is far in the future because there is still much energy available for use. Actually, the heat death will never happen, because the universe will not be left to itself. The Lord will return and replace this universe with a new one. With Him ruling and sustaining the new universe, you will not have to worry about exhausting the available energy. ###### 16C Section Review 1. What property of a system does entropy describe? 2. According to the second law of thermodynamics, what happens to the entropy of a system subject to natural processes? 3. A mixture of ice and water is contained in a near-perfect adiabatic container. As the entropy of the melting ice increases, what must happen to the entropy of the water surrounding it? 4. Briefly discuss how the free expansion of a gas in an adiabatic container increases the entropy of the gas. 5. a. What would be the likelihood of all the oxygen in your classroom clumping together in a 1 L volume in one corner? b. If it did, would the entropy of the gas be higher or lower than is normally the case? 6. The belief that matter is eternal is often a tenet of what system of philosophy? 7. As one follows the progress of total entropy in the expanding universe after the supposed big bang, what direct violation of the second law of thermodynamics must have occurred for the universe to have acquired its present form? 8. What is the flaw in some evolutionists' logic when they appeal to the statistical nature of entropy over immense periods of time as a justification for evolution? ##### 16.9 Heat Engines and the Second Law All thermodynamic processes except adiabatic processes involve exchanges of energy between a system and its surroundings. The surroundings must therefore contain either a source of thermal energy, a sink (or receiver) for thermal energy, or both. An easy way to visualize a thermal energy source or sink is to imagine a heat reservoir at a specific temperature. The reservoir is so large that no addition or subtraction of energy can change its temperature significantly. A reservoir at a higher temperature than the system, called a hot reservoir, is a source of thermal energy for the system. A reservoir at a lower temperature than the system, called a cold reservoir, is a thermal energy sink for the system. Both a hot reservoir and a cold reservoir are used to operate a heat engine. A source of thermal energy for a system must be hotter than the system. The reason is that thermal energy flows from a hotter body to a colder body. This prin- ciple agrees with human experience. If you place a glass of hot water against a glass of cold water, the cold water warms, while the hot water cools. What would you think if, after a few minutes of contact, the cold water froze and the hot water boiled? One form of the second law of thermodynamics is the principle that en- ergy flows from an area of higher concentration to an area of lower concentration. A typical heat engine requires a hot reservoir, a cold reservoir, and a working fluid (a liquid or gas). Thermal energy absorbed from the hot reservoir causes the fluid to expand against a piston or some other movable part. The expansion forces the part to move, performing mechanical work. Then, the fluid gives up thermal energy to the cold reservoir and contracts. The fluid is then ready to be heated and expand again. ##### 16.10 Early Steam Engines A steam engine is a heat engine using steam as the working fluid. For centuries men have known that steam can do work. The first steam engine, the aeolipile, was described by Hero of Alexandria, who lived about the time of Christ That's a very detailed conversion to markdown! 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