An apparatus that liquefies helium is in a room maintained at 300 K. If the helium in

Suppose 4.00 mol of an ideal gas undergoes a reversible isothermal expansion from volume V1 to volume V2  2.00V1 at temperature T  400 K. Find (a) the work done by the gas and (b) the entropy change of the gas. (c) If the expansion is reversible and adiabatic instead of isothermal, what is the entropy change of the gas?

An ideal gas undergoes a reversible isothermal expansion at 77.0 C, increasing its volume from 1.30 L to 3.40 L. The entropy change of the gas is 22.0 J/K. How many moles of gas are present?

A 2.50 mol sample of an ideal gas expands reversibly and isothermally at 360 K until its volume is doubled. What is the increase in entropy of the gas?

How much energy must be transferred as heat for a reversible isothermal expansion of an ideal gas at 132 C if the entropy of the gas increases by 46.0 J/K?

Find (a) the energy absorbed as heat and (b) the change in entropy of a 2.00 kg block of copper whose temperature is increased reversibly from 25.0C to 100C. The specific heat of copper is 386 J/kg K.

(a) What is the entropy change of a 12.0 g ice cube that melts completely in a bucket of water whose temperature is just above the freezing point of water? (b) What is the entropy change of a 5.00 g spoonful of water that evaporates completely on a hot plate whose temperature is slightly above the boiling point of water?

A 50.0 g block of copper whose temperature is 400 K is placed in an insulating box with a 100 g block of lead whose temperature is 200 K. (a) What is the equilibrium temperature of the twoblock system? (b) What is the change in the internal energy of the system between the initial state and the equilibrium state? (c) What is the change in the entropy of the system? (See Table 18-3.)

At very low temperatures, the molar specific heat CV of many solids is approximately CV  AT3 , where A depends on the particular substance. For aluminum, J/molK4 . Find the entropy change for 4.00 mol of aluminum when its temperature is raised from 5.00 K to 10.0 K.

A 10 g ice cube at 10C is placed in a lake whose temperature is 15C. Calculate the change in entropy of the cubelake system as the ice cube comes to thermal equilibrium with the lake.The specific heat of ice is 2220 J/kg K. (Hint:Will the ice cube affect the lake temperature?)

A 364 g block is put in contact with a thermal reservoir. The block is initially at a lower temperature than the reservoir. Assume that the consequent transfer of energy as heat from the reservoir to the block is reversible. Figure 20-22 gives the change in entropy S of the block until thermal equilibrium is reached.The scale of the horizontal axis is set by Ta  280 K and Tb  380 K.What is the specific heat of the block? 60 40 20 Ta T (K) Tb Figure 20-22 Problem 10.

In an experiment, 200 g of aluminum (with a specific heat of 900 J/kg K) at 100 C is mixed with 50.0 g of water at 20.0C, with the mixture thermally isolated. (a) What is the equilibrium temperature? What are the entropy changes of (b) the aluminum, (c) the water, and (d) the aluminumwater system?

A gas sample undergoes a reversible isothermal expansion. Figure 20-23 gives the change S in entropy of the gas versus the final volume Vf of the gas. The scale of the vertical axis is set by Ss  64 J/K. How many moles are in the sample? Ss 0 0.8 1.6 2.4 Vf (m3) 3.2 4.0 Figure 20-23 Problem 12.

In the irreversible process of Fig. 20-5, let the initial temperatures of the identical blocks L and R be 305.5 and 294.5 K, respectively, and let 215 J be the energy that must be transferred between the blocks in order to reach equilibrium. For the reversible processes of Fig. 20-6, what is for (a) block L, (b) its reservoir, (c) block R, (d) its reservoir, (e) the two-block system, and (f) the system of the two blocks and the two reservoirs?

(a) For 1.0 mol of a monatomic ideal gas taken through the cycle in Fig. 20-24, where V1  4.00V0, what is W/p0V0 as the gas goes from state a to state c along path abc? What is Eint/p0V0 in going (b) from b to c and (c) through one full cycle? What is S in going (d) from b to c and (e) through one full cycle? p0 Volume Pressure p0 c b a

A mixture of 1773 g of water and 227 g of ice is in an initial equilibrium state at 0.000C. The mixture is then, in a reversible process, brought to a second equilibrium state where the waterice ratio, by mass, is 1.001.00 at 0.000C. (a) Calculate the entropy change of the system during this process. (The heat of fusion for water is 333 kJ/kg.) (b) The system is then returned to the initial equilibrium state in an irreversible process (say, by using a Bunsen burner). Calculate the entropy change of the system during this process. (c) Are your answers consistent with the second law of thermodynamics?

An 8.0 g ice cube at 10C is put into a Thermos flask containing 100 cm3 of water at 20 C. By how much has the entropy of the cubewater system changed when equilibrium is reached? The specific heat of ice is 2220 J/kgK.

In Fig. 20-25, where V23  3.00V1, n moles of a diatomic ideal gas are taken through the cycle with the molecules rotating but not oscillating. What are (a) p2/p1, (b) p3/p1, and (c) T3/T1? For path 1 : 2, what are (d) W/nRT1, (e) Q/nRT1, (f) Eint/nRT1, and (g) S/nR? For path 2 : 3, what are (h) W/nRT1, (i) Q/nRT1, (j) Eint/nRT1, (k) S/nR? For path 3 : 1, what are (l) W/nRT1, (m) Q/nRT1, (n) Eint/nRT1, and (o) S/nR? 2 Isothermal V1 V23 Volume Pressure Adiabatic 1 Figure 20-25 Problem 17.

A 2.0 mol sample of an ideal monatomic gas undergoes the reversible process shown in Fig. 20-26. The scale of the vertical axis is set by Ts  400.0 K and the scale of the horizontal axis is set by Ss  20.0 J/K. (a) How much energy is absorbed as heat by the gas? (b) What is the change in the internal energy of the gas? (c) How much work is done by the gas? Entropy (J/K) Temperature (K) 0 Ts Figure 20-26 Problem 18.

Suppose 1.00 mol of a monatomic ideal gas is taken from initial pressure p1 and volume V1 through two steps: (1) an isothermal expansion to volume 2.00V1 and (2) a pressure increase to 2.00p1 at constant volume. What is Q/p1V1 for (a) step 1 and (b) step 2? What is W/p1V1 for (c) step 1 and (d) step 2? For the full process, what are (e) Eint/p1V1 and (f) S? The gas is returned to its initial state and again taken to the same final state but now through these two steps: (1) an isothermal compression to pressure 2.00p1 and (2) a volume increase to 2.00V1 at constant pressure.What is Q/p1V1 for (g) step 1 and (h) step 2? What is W/p1V1 for (i) step 1 and (j) step 2? For the full process, what are (k) Eint/p1V1 and (l) S?

Expand 1.00 mol of an monatomic gas initially at 5.00 kPa and 600 K from initial volume Vi  1.00 m3 to final volume Vf  2.00 m3 .At any instant during the expansion, the pressure p and volume V of the gas are related by p  5.00 exp[(Vi  V)/a], with p in kilopascals, Vi and V in cubic meters, and a  1.00 m3 . What are the final (a) pressure and (b) temperature of the gas? (c) How much work is done by the gas during the expansion? (d) What is S for the expansion? (Hint: Use two simple reversible processes to find S.)

Energy can be removed from water as heat at and even below the normal freezing point (0.0 C at atmospheric pressure) without causing the water to freeze; the water is then said to be supercooled. Suppose a 1.00 g water drop is supercooled until its temperature is that of the surrounding air, which is at 5.00C. The drop then suddenly and irreversibly freezes, transferring energy to the air as heat. What is the entropy change for the drop? (Hint: Use a three-step reversible process as if the water were taken through the normal freezing point.) The specific heat of ice is 2220 J/kg K.

An insulated Thermos contains 130 g of water at 80.0C. You put in a 12.0 g ice cube at 0 C to form a system of ice original water. (a) What is the equilibrium temperature of the system? What are the entropy changes of the water that was originally the ice cube (b) as it melts and (c) as it warms to the equilibrium temperature? (d) What is the entropy change of the original water as it cools to the equilibrium temperature? (e) What is the net entropy change of the ice original water system as it reaches the equilibrium temperature?

A Carnot engine whose low-temperature reservoir is at 17C has an efficiency of 40%. By how much should the temperature of the high-temperature reservoir be increased to increase the efficiency to 50%?

A Carnot engine absorbs 52 kJ as heat and exhausts 36 kJ as heat in each cycle. Calculate (a) the engines efficiency and (b) the work done per cycle in kilojoules.

A Carnot engine has an efficiency of 22.0%. It operates between constant-temperature reservoirs differing in temperature by 75.0 C . What is the temperature of the (a) lower-temperature and (b) higher-temperature reservoir?

In a hypothetical nuclear fusion reactor, the fuel is deuterium gas at a temperature of 7  108 K. If this gas could be used to operate a Carnot engine with TL  100 C, what would be the engines efficiency? Take both temperatures to be exact and report your answer to seven significant figures.

A Carnot engine operates between 235 C and 115 C, absorbing 6.30 104 J per cycle at the higher temperature. (a) What is the efficiency of the engine? (b) How much work per cycle is this engine capable of performing?

In the first stage of a two-stage Carnot engine, energy is absorbed as heat Q1 at temperature T1, work W1 is done, and energy is expelled as heat Q2 at a lower temperature T2. The second stage absorbs that energy as heat Q2, does work W2, and expels energy as heat Q3 at a still lower temperature T3. Prove that the efficiency of the engine is (T1  T3)/T1.

Figure 20-27 shows a reversible cycle through which 1.00 mol of a monatomic ideal gas is taken. Assume that p  2p0, V  2V0, p0  1.01  105 Pa, and V0  0.0225 m3 . Calculate (a) the work done during the cycle, (b) the energy added as heat during stroke abc, and (c) the efficiency of the cycle. (d) What is the efficiency of a Carnot engine operating between the highest and lowest temperatures that occur in the cycle? (e) Is this greater than or less than the efficiency calculated in (c)? V0, p0 Volume Pressure b Figure 20-27 Problem 29.

A 500 W Carnot engine operates between constanttemperature reservoirs at 100 C and 60.0 C.What is the rate at which energy is (a) taken in by the engine as heat and (b) exhausted by the engine as heat?

The efficiency of a particular car engine is 25% when the engine does 8.2 kJ of work per cycle.Assume the process is reversible. What are (a) the energy the engine gains per cycle as heat Qgain from the fuel combustion and (b) the energy the engine loses per cycle as heat Qlost? If a tune-up increases the efficiency to 31%, what are (c) Qgain and (d) Qlost at the same work value?

A Carnot engine is set up to produce a certain work W   per cycle. In each cycle, energy in the form of heat QH is transferred to the working substance of the engine from the higher-temperature thermal reservoir, which is at an adjustable temperature TH. The lower-temperature thermal reservoir is maintained at temperature TL  250 K. Figure 20-28 gives QH for a range of TH. The scale of the vertical axis is set by QHs  6.0 kJ. If TH is set at 550 K, what is QH? Q Hs 0 250 300 TH (K) 350 Figure 20-28 Problem 32.

Figure 20-29 shows a reversible cycle through which 1.00 mol of a monatomic ideal gas is taken. Volume Vc  8.00Vb. Process bc is an adiabatic expansion, with pb  10.0 atm and Vb  1.00  103 m3 . For the cycle, find (a) the energy added to the gas as heat, (b) the energy leaving the gas as heat, (c) the net work done by the gas, and (d) the efficiency of the cycle. a c Adiabatic Vb Vc p Figure 20-29 Problem 33.

An ideal gas (1.0 mol) is the working substance in an engine that operates on the cycle shown in Fig. 20-30. Processes BC and DA are reversible and adiabatic. (a) Is the gas monatomic, diatomic, or polyatomic? (b) What is the engine efficiency? V0 16V0 Volume Pressure p0/32 2V0 8V0 p0 A Figure 20-30 Problem 34

The cycle in Fig. 20-31 represents the operation of a gasoline internal combustion engine. Volume V3  4.00V1. Assume the gasolineair intake mixture is an ideal gas with g  1.30. What are the ratios (a) T2/T1, (b) T3/T1, (c) T4/T1, (d) p3/p1, and (e) p4/p1? (f) What is the engine efficiency? 3.00p1 Volume Pressure p1 Adiabatic 1 3 4 Spark Intake Figure 20-31 Problem 35.

How much work must be done by a Carnot refrigerator to transfer 1.0 J as heat (a) from a reservoir at 7.0 C to one at 27 C, (b) from a reservoir at 73 C to one at 27 C, (c) from a reservoir at 173 C to one at 27 C, and (d) from a reservoir at 223 C to one at 27 C?

A heat pump is used to heat a building. The external temperature is less than the internal temperature. The pumps coefficient of performance is 3.8, and the heat pump delivers 7.54 MJ as heat to the building each hour. If the heat pump is a Carnot engine working in reverse, at what rate must work be done to run it?

The electric motor of a heat pump transfers energy as heat from the outdoors, which is at 5.0 C, to a room that is at 17 C. If the heat pump were a Carnot heat pump (a Carnot engine working in reverse), how much energy would be transferred as heat to the room for each joule of electric energy consumed?

A Carnot air conditioner takes energy from the thermal energy of a room at 70 F and transfers it as heat to the outdoors, which is at 96 F. For each joule of electric energy required to operate the air conditioner, how many joules are removed from the room?

To make ice, a freezer that is a reverse Carnot engine extracts 42 kJ as heat at 15 C during each cycle, with coefficient of performance 5.7. The room temperature is 30.3 C. How much (a) energy per cycle is delivered as heat to the room and (b) work per cycle is required to run the freezer?

An air conditioner operating between 93 F and 70 F is rated at 4000 Btu/h cooling capacity. Its coefficient of performance is 27% of that of a Carnot refrigerator operating between the same two temperatures.What horsepower is required of the air conditioner motor?

The motor in a refrigerator has a power of 200 W. If the freezing compartment is at 270 K and the outside air is at 300 K, and assuming the efficiency of a Carnot refrigerator, what is the maximum amount of energy that can be extracted as heat from the freezing compartment in 10.0 min?

Figure 20-32 represents a Carnot engine that works between temperatures T1 400 K and T2 150 K and drives a Carnot refrigerator that works between temperatures T3  325 K and T4  225 K. What is the ratio Q3/Q1? T1 T2 Q 1 Q 2 W T4 Q 3 Q 4 Engine Refrigerator Figure 20-32 Problem 43.

(a) During each cycle, a Carnot engine absorbs 750 J as heat from a high-temperature reservoir at 360 K, with the low-temperature reservoir at 280 K. How much work is done per cycle? (b) The engine is then made to work in reverse to function as a Carnot refrigerator between those same two reservoirs. During each cycle, how much work is required to remove 1200 J as heat from the low-temperature reservoir?

Construct a table like Table 20-1 for eight molecules.

A box contains N identical gas molecules equally divided between its two halves. For N  50, what are (a) the multiplicity W of the central configuration, (b) the total number of microstates, and (c) the percentage of the time the system spends in the central configuration? For N  100, what are (d) W of the central configuration, (e) the total number of microstates, and (f) the percentage of the time the system spends in the central configuration? For N  200, what are (g) W of the central configuration, (h) the total number of microstates, and (i) the percentage of the time the system spends in the central configuration? ( j) Does the time spent in the central configuration increase or decrease with an increase in N?

A box contains N gas molecules. Consider the box to be divided into three equal parts. (a) By extension of Eq. 20-20, write a formula for the multiplicity of any given configuration. (b) Consider two configurations: configuration A with equal numbers of molecules in all three thirds of the box, and configuration B with equal numbers of molecules in each half of the box divided into two equal parts rather than three. What is the ratio WA/WB of the multiplicity of configuration A to that of configuration B? (c) Evaluate WA/WB for N  100. (Because 100 is not evenly divisible by 3, put 34 molecules into one of the three box parts of configuration A and 33 in each of the other two parts.)

Four particles are in the insulated box of Fig. 20-17. What are (a) the least multiplicity, (b) the greatest multiplicity, (c) the least entropy, and (d) the greatest entropy of the four-particle system?

A cylindrical copper rod of length 1.50 m and radius 2.00 cm is insulated to prevent heat loss through its curved surface. One end is attached to a thermal reservoir fixed at 300 C; the other is attached to a thermal reservoir fixed at 30.0 C. What is the rate at which entropy increases for the rodreservoirs system?

Suppose 0.550 mol of an ideal gas is isothermally and reversibly expanded in the four situations given below. What is the change in the entropy of the gas for each situation? Situation (a) (b) (c) (d) Temperature (K) 250 350 400 450 Initial volume (cm3 ) 0.200 0.200 0.300 0.300 Final volume (cm3 ) 0.800 0.800 1.20 1.20

As a sample of nitrogen gas (N2) undergoes a temperature increase at constant volume, the distribution of molecular speeds increases. That is, the probability distribution function P(v) for the molecules spreads to higher speed values, as suggested in Fig. 19-8b. One way to report the spread in P(v) is to measure the difference v between the most probable speed vP and the rms speed vrms. When P(v) spreads to higher speeds, v increases. Assume that the gas is ideal and the N2 molecules rotate but do not oscillate. For 1.5 mol, an initial temperature of 250 K, and a final temperature of 500 K, what are (a) the initial difference vi , (b) the final difference vf, and (c) the entropy change S for the gas?

Suppose 1.0 mol of a monatomic ideal gas initially at 10 L and 300 K is heated at constant volume to 600 K, allowed to expand isothermally to its initial pressure, and finally compressed at constant pressure to its original volume, pressure, and temperature. During the cycle, what are (a) the net energy entering the system (the gas) as heat and (b) the net work done by the gas? (c) What is the efficiency of the cycle?

Suppose that a deep shaft were drilled in Earths crust near one of the poles, where the surface temperature is 40 C, to a depth where the temperature is 800 C. (a) What is the theoretical limit to the efficiency of an engine operating between these temperatures? (b) If all the energy released as heat into the lowtemperature reservoir were used to melt ice that was initially at 40 C, at what rate could liquid water at 0C be produced by a 100 MW power plant (treat it as an engine)? The specific heat of ice is 2220 J/kg K; waters heat of fusion is 333 kJ/kg. (Note that the engine can operate only between 0C and 800C in this case. Energy exhausted at 40C cannot warm anything above 40C.)

What is the entropy change for 3.20 mol of an ideal monatomic gas undergoing a reversible increase in temperature from 380 K to 425 K at constant volume?

A 600 g lump of copper at 80.0C is placed in 70.0 g of water at 10.0 C in an insulated container. (See Table 18-3 for specific heats.) (a) What is the equilibrium temperature of the copper water system? What entropy changes do (b) the copper, (c) the water, and (d) the copperwater system undergo in reaching the equilibrium temperature?

Figure 20-33 gives the force magnitude F versus stretch distance x for a rubber band, with the scale of the F axis set by Fs  1.50 N and the scale of the x axis set by xs  3.50 cm. The temperature is 2.00 C. When the rubber band is stretched by x  1.70 cm, at what rate does the entropy of the rubber band change during a small additional stretch? F (N) Fs 0 x (cm) xs Figure 20-33 Problem 56.

The temperature of 1.00 mol of a monatomic ideal gas is raised reversibly from 300 K to 400 K, with its volume kept constant.What is the entropy change of the gas?

Repeat Problem 57, with the pressure now kept constant.

A 0.600 kg sample of water is initially ice at temperature20C. What is the samples entropy change if its temperature is increased to 40 C?

A three-step cycle is undergone by 3.4 mol of an ideal diatomic gas: (1) the temperature of the gas is increased from 200 K to 500 K at constant volume; (2) the gas is then isothermally expanded to its original pressure; (3) the gas is then contracted at constant pressure back to its original volume.Throughout the cycle, the molecules rotate but do not oscillate.What is the efficiency of the cycle?

An inventor has built an engine X and claims that its efficiency X is greater than the efficiency of an ideal engine operating between the same two temperatures. Suppose you couple engine X to an ideal refrigerator (Fig. 20-34a) and adjust the cycle of engine X so that the work per cycle it provides equals the work per cycle required by the ideal refrigerator.Treat this combination as a single unit and show that if the inventors claim were true (if X  ), the combined unit would act as a perfect refrigerator (Fig. 20-34b), transferring energy as heat from the low-temperature reservoir to the high-temperature reservoir without the need for work. (b) TH Ideal refrigerator Perfect W refrigerator Q H Q Figure 20-34 Problem 61.

Suppose 2.00 mol of a diatomic gas is taken reversibly around the cycle shown in the TS diagram of Fig. 20-35, where S1  6.00 J/K and S2  8.00 J/K. The molecules do not rotate or oscillate. What is the energy transferred as heat Q for (a) path 1 : 2, (b) path 2 : 3, and (c) the full cycle? (d) What is the work W for the isothermal process? The volume V1 in state 1 is 0.200 m3 . What is the volume in (e) state 2 and (f) state 3? What is the change Eint for (g) path 1 : 2, (h) path 2 : 3, and (i) the full cycle? (Hint: (h) can be done with one or two lines of calculation using Module 19-7 or with a page of calculation using Module 19-9.) (j) What is the work W for the adiabatic process? 350 300 1 2 3 S1 S2 Entropy (J/K) Temperature (K) Figure 20-35 Problem 62.

A three-step cycle is undergone reversibly by 4.00 mol of an ideal gas: (1) an adiabatic expansion that gives the gas 2.00 times its initial volume, (2) a constant-volume process, (3) an isothermal compression back to the initial state of the gas. We do not know whether the gas is monatomic or diatomic; if it is diatomic, we do not know whether the molecules are rotating or oscillating.What are the entropy changes for (a) the cycle,(b) process 1,(c) process 3,and (d) process 2?

(a) A Carnot engine operates between a hot reservoir at 320 K and a cold one at 260 K. If the engine absorbs 500 J as heat per cycle at the hot reservoir, how much work per cycle does it deliver? (b) If the engine working in reverse functions as a refrigerator between the same two reservoirs, how much work per cycle must be supplied to remove 1000 J as heat from the cold reservoir?

A 2.00 mol diatomic gas initially at 300 K undergoes this cycle: It is (1) heated at constant volume to 800 K, (2) then allowed to expand isothermally to its initial pressure, (3) then compressed at constant pressure to its initial state. Assuming the gas molecules neither rotate nor oscillate, find (a) the net energy transferred as heat to the gas, (b) the net work done by the gas, and (c) the efficiency of the cycle.

An ideal refrigerator does 150 J of work to remove 560 J as heat from its cold compartment. (a) What is the refrigerators coefficient of performance? (b) How much heat per cycle is exhausted to the kitchen?

Suppose that 260 J is conducted from a constant-temperature reservoir at 400 K to one at (a) 100 K, (b) 200 K, (c) 300 K, and (d) 360 K. What is the net change in entropy Snet of the reservoirs in each case? (e) As the temperature difference of the two reservoirs decreases, does Snet increase, decrease, or remain the same?

An apparatus that liquefies helium is in a room maintained at 300 K. If the helium in the apparatus is at 4.0 K, what is the minimum ratio Qto/Qfrom, where Qto is the energy delivered as heat to the room and Qfrom is the energy removed as heat from the helium?

A brass rod is in thermal contact with a constant-temperature reservoir at 130 C at one end and a constant-temperature reservoir at 24.0 C at the other end. (a) Compute the total change in entropy of the rodreservoirs system when 5030 J of energy is conducted through the rod, from one reservoir to the other. (b) Does the entropy of the rod change?

A 45.0 g block of tungsten at 30.0 C and a 25.0 g block of silver at 120 C are placed together in an insulated container. (See Table 18-3 for specific heats.) (a) What is the equilibrium temperature? What entropy changes do (b) the tungsten, (c) the silver, and (d) the tungstensilver system undergo in reaching the equilibrium temperature?

A box contains N molecules. Consider two configurations: configuration A with an equal division of the molecules between the two halves of the box, and configuration B with 60.0% of the molecules in the left half of the box and 40.0% in the right half. For N  50, what are (a) the multiplicity WA of configuration A, (b) the multiplicity WB of configuration B, and (c) the ratio fB/A of the time the system spends in configuration B to the time it spends in configuration A? For N  100, what are (d) WA, (e) WB, and (f) fB/A? For N  200, what are (g) WA, (h) WB, and (i) fB/A? ( j) With increasing N, does f increase, decrease, or remain the same?

Calculate the efficiency of a fossil-fuel power plant that consumes 380 metric tons of coal each hour to produce useful work at the rate of 750 MW. The heat of combustion of coal (the heat due to burning it) is 28 MJ/kg.

A Carnot refrigerator extracts 35.0 kJ as heat during each cycle, operating with a coefficient of performance of 4.60. What are (a) the energy per cycle transferred as heat to the room and (b) the work done per cycle?

A Carnot engine whose high-temperature reservoir is at 400 K has an efficiency of 30.0%. By how much should the temperature of the low-temperature reservoir be changed to increase the efficiency to 40.0%?

System A of three particles and system B of five particles are in insulated boxes like that in Fig. 20-17.What is the least multiplicity W of (a) system A and (b) system B? What is the greatest multiplicity W of (c) A and (d) B? What is the greatest entropy of (e) A and (f) B?

Figure 20-36 shows a Carnot cycle on a T-S diagram, with a scale set by Ss  0.60 J/K. For a full cycle, find (a) the net heat transfer and (b) the net work done by the system. ) 400 300 200 100 0 Ss Figure 20-36 Problem 76.

Find the relation between the efficiency of a reversible ideal heat engine and the coefficient of performance of the reversible refrigerator obtained by running the engine backwards.

A Carnot engine has a power of 500 W. It operates between heat reservoirs at 100 C and 60.0 C. Calculate (a) the rate of heat input and (b) the rate of exhaust heat output.

In a real refrigerator, the low-temperature coils are at 13 C, and the compressed gas in the condenser is at 26 C. What is the theoretical coefficient of performance?