A sample of an ideal gas expands isothermally, doubling in

The second law of thermodynamics implies that the coefficient of performance of a refrigerator must be what? (a) less than 1 (b) less than or equal to 1 (c) greater than or equal to 1 (d) finite (e) greater than 0

Assume a sample of an ideal gas is at room temperature. What action will necessarily make the entropy of the sample increase? (a) Transfer energy into it by heat. (b) Transfer energy into it irreversibly by heat. (c) Do work on it. (d) Increase either its temperature or its volume, without letting the other variable decrease. (e) None of those choices is correct

A refrigerator has 18.0 kJ of work done on it while 115 kJ of energy is transferred from inside its interior. What is its coefficient of performance? (a) 3.40 (b) 2.80 (c) 8.90 (d) 6.40 (e) 5.20

Of the following, which is not a statement of the second law of thermodynamics? (a) No heat engine operating in a cycle can absorb energy from a reservoir and use it entirely to do work. (b) No real engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs. (c)When a system undergoes a change in state, the change in the internal energy of the system is the sum of the energy transferred to the system by heat and the work done on the system. (d)The entropy of the Universe increases in all natural processes. (e) Energy will not spontaneously transfer by heat from a cold object to a hot object.

Consider cyclic processes completely characterized by each of the following net energy inputs and outputs. In each case, the energy transfers listed are the only ones occurring. Classify each process as (a) possible, (b) impossible according to the first law of thermodynamics, (c) impossible according to the second law of thermodynamics, or (d) impossible according to both the first and second laws. (i) Input is 5 J of work, and output is 4 J of work. (ii) Input is 5 J of work, and output is 5 J of energy transferred by heat. (iii) Input is 5 J of energy transferred by electrical transmission, and output is 6 J of work. (iv) Input is 5 J of energy transferred by heat, and output is 5 J of energy transferred by heat. (v) Input is 5 J of energy transferred by heat, and output is 5 J of work. (vi) Input is 5 J of energy transferred by heat, and output is 3 J of work plus 2 J of energy transferred by heat.

A compact air-conditioning unit is placed on a table inside a well-insulated apartment and is plugged in and turned on. What happens to the average temperature of the apartment? (a) It increases. (b) It decreases. (c) It remains constant. (d) It increases until the unit warms up and then decreases. (e) The answer depends on the initial temperature of the apartment.

A steam turbine operates at a boiler temperature of 450 K and an exhaust temperature of 300 K. What is the maximum theoretical efficiency of this system? (a) 0.240 (b) 0.500 (c) 0.333 (d) 0.667 (e) 0.150

A thermodynamic process occurs in which the entropy of a system changes by 28 J/K. According to the second law of thermodynamics, what can you conclude about the entropy change of the environment? (a) It must be 18 J/K or less. (b) It must be between 18 J/K and 0. (c) It must be equal to 18 J/K. (d) It must be 18 J/K or more. (e) It must be zero.

A sample of a monatomic ideal gas is contained in a cylinder with a piston. Its state is represented by the dot in the PV diagram shown in Figure OQ22.9. Arrows A through E represent isobaric, isothermal, adiabatic, and isovolumetric processes that the sample can undergo. In each process except D, the volume changes by a factor of 2. All five processes are reversible. Rank the processes according to the change in entropy of the gas from the largest positive value to the largest-magnitude negative value. In your rankings, display any cases of equality.

An engine does 15.0 kJ of work while exhausting 37.0 kJ to a cold reservoir. What is the efficiency of the engine? (a) 0.150 (b) 0.288 (c) 0.333 (d) 0.450 (e) 1.20

The arrow OA in the PV diagram shown in Figure OQ22.11 represents a reversible adiabatic expansion of an ideal gas. The same sample of gas, starting from the same state O, now undergoes an adiabatic free expansion to the same final volume. What point on the diagram could represent the final state of the gas? (a) the same point A as for the reversible expansion (b) point B (c) point C (d) any of those choices (e) none of those choices

(a) If you shake a jar full of jelly beans of different sizes, the larger beans tend to appear near the top and the smaller ones tend to fall to the bottom. Why? (b) Does this process violate the second law of thermodynamics?

What are some factors that affect the efficiency of automobile engines?

A heat engine operates between a reservoir at 25.0C and one at 375C. What is the maximum efficiency possible for this engine?

One of the most efficient heat engines ever built is a coal-fired steam turbine in the Ohio River valley, operating between 1 870C and 430C. (a) What is its maximum theoretical efficiency? (b) The actual efficiency of the engine is 42.0%. How much mechanical power does the engine deliver if it absorbs 1.40 3 105 J of energy each second from its hot reservoir?

Why is the following situation impossible? An inventor comes to a patent office with the claim that her heat engine, which employs water as a working substance, has a thermodynamic efficiency of 0.110. Although this efficiency is low compared with typical automobile engines, she explains that her engine operates between an energy reservoir at room temperature and a waterice mixture at atmospheric pressure and therefore requires no fuel other than that to make the ice. The patent is approved, and working prototypes of the engine prove the inventors efficiency claim.

A Carnot engine has a power output of 150 kW. The engine operates between two reservoirs at 20.0C and 500C. (a) How much energy enters the engine by heat per hour? (b) How much energy is exhausted by heat per hour?

A Carnot engine has a power output P. The engine operates between two reservoirs at temperature Tc and Th. (a) How much energy enters the engine by heat in a time interval Dt? (b) How much energy is exhausted by heat in the time interval Dt?

What is the coefficient of performance of a refrigerator that operates with Carnot efficiency between temperatures 23.00C and 127.0C?

An ideal refrigerator or ideal heat pump is equivalent to a Carnot engine running in reverse. That is, energy |Q c| is taken in from a cold reservoir and energy |Q h | is rejected to a hot reservoir. (a) Show that the work that must be supplied to run the refrigerator or heat pump is W 5 Th 2 Tc Tc 0 Q c 0 (b) Show that the coefficient of performance (COP) of the ideal refrigerator is COP 5 Tc Th 2 Tc

What is the maximum possible coefficient of performance of a heat pump that brings energy from outdoors at 23.00C into a 22.0C house? Note: The work done to run the heat pump is also available to warm the house.

How much work does an ideal Carnot refrigerator require to remove 1.00 J of energy from liquid helium at 4.00 K and expel this energy to a room-temperature (293-K) environment?

If a 35.0%-efficient Carnot heat engine (Fig. 22.2) is run in reverse so as to form a refrigerator (Fig. 22.4), what would be this refrigerators coefficient of performance?

A power plant operates at a 32.0% efficiency during the summer when the seawater used for cooling is at 20.0C. The plant uses 350C steam to drive turbines. If the plants efficiency changes in the same proportion as the ideal efficiency, what would be the plants efficiency in the winter, when the seawater is at 10.0C?

A heat engine is being designed to have a Carnot efficiency of 65.0% when operating between two energy reservoirs. (a) If the temperature of the cold reservoir is 20.0C, what must be the temperature of the hot reservoir? (b)Can the actual efficiency of the engine be equal to 65.0%? Explain.

A Carnot heat engine operates between temperatures Th and Tc. (a) If Th 5 500 K and Tc 5 350 K, what is the efficiency of the engine? (b) What is the change in its efficiency for each degree of increase in Th above 500 K? (c) What is the change in its efficiency for each degree of change in Tc? (d) Does the answer to part (c) depend on Tc? Explain.

An ideal gas is taken through a Carnot cycle. The isothermal expansion occurs at 250C, and the isothermal compression takes place at 50.0C. The gas takes in 1.20 3 103 J of energy from the hot reservoir during the isothermal expansion. Find (a) the energy expelled to the cold reservoir in each cycle and (b) the net work done by the gas in each cycle.

An electric power plant that would make use of the temperature gradient in the ocean has been proposed. The system is to operate between 20.0C (surfacewater temperature) and 5.00C (water temperature at a depth of about 1 km). (a) What is the maximum efficiency of such a system? (b) If the electric power output of the plant is 75.0 MW, how much energy is taken in from the warm reservoir per hour? (c) In view of your answer to part (a), explain whether you think such a system is worthwhile. Note that the fuel is free.

A heat engine operates in a Carnot cycle between 80.0C and 350C. It absorbs 21 000 J of energy per cycle from the hot reservoir. The duration of each cycle is 1.00 s. (a) What is the mechanical power output of this engine? (b) How much energy does it expel in each cycle by heat?

Suppose you build a two-engine device with the exhaust energy output from one heat engine supplying the input energy for a second heat engine. We say that the two engines are running in series. Let e1 and e2 represent the efficiencies of the two engines. (a) The overall efficiency of the two-engine device is defined as the total work output divided by the energy put into the first engine by heat. Show that the overall efficiency e is given by e 5 e1 1 e2 2 e1e2 What If? For parts (b) through (e) that follow, assume the two engines are Carnot engines. Engine 1 operates between temperatures Th and Ti . The gas in engine 2 varies in temperature between Ti and Tc. In terms of the temperatures, (b) what is the efficiency of the combination engine? (c) Does an improvement in net efficiency result from the use of two engines instead of one? (d) What value of the intermediate temperature Ti results in equal work being done by each of the two engines in series? (e) What value of Ti results in each of the two engines in series having the same efficiency?

Argon enters a turbine at a rate of 80.0 kg/min, a temperature of 800C, and a pressure of 1.50 MPa. It expands adiabatically as it pushes on the turbine blades and exits at pressure 300 kPa. (a) Calculate its temperature at exit. (b) Calculate the (maximum) power output of the turning turbine. (c) The turbine is one component of a model closed-cycle gas turbine engine. Calculate the maximum efficiency of the engine.

At point A in a Carnot cycle, 2.34 mol of a monatomic ideal gas has a pressure of 1 400 kPa, a volume of 10.0 L, and a temperature of 720 K. The gas expands isothermally to point B and then expands adiabatically to point C, where its volume is 24.0 L. An isothermal compression brings it to point D, where its volume is 15.0 L. An adiabatic process returns the gas to point A. (a) Determine all the unknown pressures, volumes, and temperatures as you fill in the following table: P V T A 1 400 kPa 10.0 L 720 K B C 24.0 L D 15.0 L (b) Find the energy added by heat, the work done by the engine, and the change in internal energy for each of the steps A S B, B S C, C S D, and D S A. (c) Calculate the efficiency Wnet/|Q h|. (d) Show that the efficiency is equal to 1 2 TC /TA, the Carnot efficiency

An electric generating station is designed to have an electric output power of 1.40 MW using a turbine with two-thirds the efficiency of a Carnot engine. The exhaust energy is transferred by heat into a cooling tower at 110C. (a) Find the rate at which the station exhausts energy by heat as a function of the fuel combustion temperature Th. (b) If the firebox is modified to run hotter by using more advanced combustion technology, how does the amount of energy exhaust change? (c) Find the exhaust power for Th 5 800C. (d) Find the value of Th for which the exhaust power would be only half as large as in part (c). (e) Find the value of Th for which the exhaust power would be one-fourth as large as in part (c)

An ideal (Carnot) freezer in a kitchen has a constant temperature of 260 K, whereas the air in the kitchen has a constant temperature of 300 K. Suppose the insulation for the freezer is not perfect but rather conducts energy into the freezer at a rate of 0.150 W. Determine the average power required for the freezers motor to maintain the constant temperature in the freezer.

A heat pump used for heating shown in Figure P22.35 is essentially an air conditioner installed backward. It extracts energy from colder air outside and deposits it in a warmer room. Suppose the ratio of the actual energy entering the room to the work done by the devices motor is 10.0% of the theoretical maximum ratio. Determine the energy entering the room per joule of work done by the motor given that the inside temperature is 20.0C and the outside temperature is 25.00C.

A gasoline engine has a compression ratio of 6.00. (a) What is the efficiency of the engine if it operates in an idealized Otto cycle? (b) What If? If the actual efficiency is 15.0%, what fraction of the fuel is wasted as a result of friction and energy transfers by heat that could be avoided in a reversible engine? Assume complete combustion of the airfuel mixture.

In a cylinder of an automobile engine, immediately after combustion the gas is confined to a volume of 50.0 cm3 and has an initial pressure of 3.00 3 106 Pa. The piston moves outward to a final volume of 300 cm3, and the gas expands without energy transfer by heat. (a) What is the final pressure of the gas? (b) How much work is done by the gas in expanding?

An idealized diesel engine operates in a cycle known as the air-standard diesel cycle shown in Figure P22.38. Fuel is sprayed into the cylinder at the point of maximum compression, B. Combustion occurs during the expansion B S C, which is modeled as an isobaric process. Show that the efficiency of an engine operating in this idealized diesel cycle is e 5 1 2 1 g a TD 2 TA TC 2 TB b

Prepare a table like Table 22.1 by using the same procedure (a) for the case in which you draw three marbles from your bag rather than four and (b) for the case in which you draw five marbles rather than four.

(a) Prepare a table like Table 22.1 for the following occurrence. You toss four coins into the air simultaneously and then record the results of your tosses in terms of the numbers of heads (H) and tails (T) that result. For example, HHTH and HTHH are two possible ways in which three heads and one tail can be achieved. (b) On the basis of your table, what is the most probable result recorded for a toss?

If you roll two dice, what is the total number of ways in which you can obtain (a) a 12 and (b) a 7?

An ice tray contains 500 g of liquid water at 0C. Calculate the change in entropy of the water as it freezes slowly and completely at 0C.

A Styrofoam cup holding 125 g of hot water at 100C cools to room temperature, 20.0C. What is the change in entropy of the room? Neglect the specific heat of the cup and any change in temperature of the room

A 1.00-kg iron horseshoe is taken from a forge at 900C and dropped into 4.00 kg of water at 10.0C. Assuming that no energy is lost by heat to the surroundings, determine the total entropy change of the horseshoeplus-water system. (Suggestion: Note that dQ 5 mc dT.)

A 1 500-kg car is moving at 20.0 m/s. The driver brakes to a stop. The brakes cool off to the temperature of the surrounding air, which is nearly constant at 20.0C. What is the total entropy change?

Two 2.00 3 103-kg cars both traveling at 20.0 m/s undergo a head-on collision and stick together. Find the change in entropy of the surrounding air resulting from the collision if the air temperature is 23.0C. Ignore the energy carried away from the collision by sound.

A 70.0-kg log falls from a height of 25.0 m into a lake. If the log, the lake, and the air are all at 300 K, find the change in entropy of the air during this process.

A 1.00-mol sample of H2 gas is contained in the left side of the container shown in Figure P22.48, which has equal volumes on the left and right. The right side is evacuated. When the valve is opened, the gas streams into the right side. (a) What is the entropy change of the gas? (b) Does the temperature of the gas change? Assume the container is so large that the hydrogen behaves as an ideal gas.

A 2.00-L container has a center partition that divides it into two equal parts as shown in Figure P22.49. The left side contains 0.044 0 mol of H2 gas, and the right side contains 0.044 0 mol of O2 gas. Both gases are at room temperature and at atmospheric pressure. The partition is removed, and the gases are allowed to mix. What is the entropy increase of the system?

What change in entropy occurs when a 27.9-g ice cube at 212C is transformed into steam at 115C?

Calculate the change in entropy of 250 g of water warmed slowly from 20.0C to 80.0C

How fast are you personally making the entropy of the Universe increase right now? Compute an order-ofmagnitude estimate, stating what quantities you take as data and the values you measure or estimate for them.

When an aluminum bar is connected between a hot reservoir at 725 K and a cold reservoir at 310 K, 2.50 kJ of energy is transferred by heat from the hot reservoir to the cold reservoir. In this irreversible process, calculate the change in entropy of (a) the hot reservoir, (b) the cold reservoir, and (c) the Universe, neglecting any change in entropy of the aluminum rod.

When a metal bar is connected between a hot reservoir at Th and a cold reservoir at Tc , the energy transferred by heat from the hot reservoir to the cold reservoir is Q. In this irreversible process, find expressions for the change in entropy of (a) the hot reservoir, (b) the cold reservoir, and (c) the Universe, neglecting any change in entropy of the metal rod.

The temperature at the surface of the Sun is approximately 5 800 K, and the temperature at the surface of the Earth is approximately 290 K. What entropy change of the Universe occurs when 1.00 3 103 J of energy is transferred by radiation from the Sun to the Earth?

Calculate the increase in entropy of the Universe when you add 20.0 g of 5.00C cream to 200 g of 60.0C coffee. Assume that the specific heats of cream and coffee are both 4.20 J/g ? C.

How much work is required, using an ideal Carnot refrigerator, to change 0.500 kg of tap water at 10.0C into ice at 220.0C? Assume that the freezer compartment is held at 220.0C and that the refrigerator exhausts energy into a room at 20.0C.

A steam engine is operated in a cold climate where the exhaust temperature is 0C. (a) Calculate the theoretical maximum efficiency of the engine using an intake steam temperature of 100C. (b) If, instead, superheated steam at 200C is used, find the maximum possible efficiency

The energy absorbed by an engine is three times greater than the work it performs. (a) What is its thermal efficiency? (b) What fraction of the energy absorbed is expelled to the cold reservoir?

Every second at Niagara Falls, some 5.00 3 103 m3 of water falls a distance of 50.0 m. What is the increase in entropy of the Universe per second due to the falling water? Assume the mass of the surroundings is so great that its temperature and that of the water stay nearly constant at 20.0C. Also assume a negligible amount of water evaporates.

Find the maximum (Carnot) efficiency of an engine that absorbs energy from a hot reservoir at 545C and exhausts energy to a cold reservoir at 185C.

In 1993, the U.S. government instituted a requirement that all room air conditioners sold in the United States must have an energy efficiency ratio (EER) of 10 or higher. The EER is defined as the ratio of the cooling capacity of the air conditioner, measured in British thermal units per hour, or Btu/h, to its electrical power requirement in watts. (a) Convert the EER of 10.0 to dimensionless form, using the conversion 1 Btu 5 1 055 J. (b) What is the appropriate name for this dimensionless quantity? (c) In the 1970s, it was common to find room air conditioners with EERs of 5 or lower. State how the operating costs compare for 10 000-Btu/h air conditioners with EERs of 5.00 and 10.0. Assume each air conditioner operates for 1 500 h during the summer in a city where electricity costs 17.0 per kWh.

Energy transfers by heat through the exterior walls and roof of a house at a rate of 5.00 3 103 J/s 5 5.00 kW when the interior temperature is 22.0C and the outside temperature is 25.00C. (a) Calculate the electric power required to maintain the interior temperature at 22.0C if the power is used in electric resistance heaters that convert all the energy transferred in by electrical transmission into internal energy. (b) What If? Calculate the electric power required to maintain the interior temperature at 22.0C if the power is used to drive an electric motor that operates the compressor of a heat pump that has a coefficient of performance equal to 60.0% of the Carnot-cycle value.

One mole of neon gas is heated from 300 K to 420 K at constant pressure. Calculate (a) the energy Q transferred to the gas, (b) the change in the internal energy of the gas, and (c) the work done on the gas. Note that neon has a molar specific heat of CP 5 20.79 J/mol ? K for a constant-pressure process.

An airtight freezer holds n moles of air at 25.0C and 1.00 atm. The air is then cooled to 218.0C. (a) What is the change in entropy of the air if the volume is held constant? (b) What would the entropy change be if the pressure were maintained at 1.00 atm during the cooling?

Suppose an ideal (Carnot) heat pump could be constructed for use as an air conditioner. (a) Obtain an expression for the coefficient of performance (COP) for such an air conditioner in terms of Th and Tc. (b) Would such an air conditioner operate on a smaller energy input if the difference in the operating temperatures were greater or smaller? (c) Compute the COP for such an air conditioner if the indoor temperature is 20.0C and the outdoor temperature is 40.0C.

In 1816, Robert Stirling, a Scottish clergyman, patented the Stirling engine, which has found a wide variety of applications ever since, including current use in solar energy collectors to transform sunlight into electricity. Fuel is burned externally to warm one of the engines two cylinders. A fixed quantity of inert gas moves cyclically between the cylinders, expanding in the hot one and contracting in the cold one. Figure P22.67 represents a model for its thermodynamic cycle. Consider n moles of an ideal monatomic gas being taken once through the cycle, consisting of two isothermal processes at temperatures 3Ti and Ti and two constant-volume processes. Let us find the efficiency of this engine. (a) Find the energy transferred by heat into the gas during the isovolumetric process AB. (b) Find the energy transferred by heat into the gas during the isothermal process BC. (c) Find the energy transferred by heat into the gas during the isovolumetric process CD. (d) Find the energy transferred by heat into the gas during the isothermal process DA. (e) Identify which of the results from parts (a) through (d) are positive and evaluate the energy input to the engine by heat. (f) From the first law of thermodynamics, find the work done by the engine. (g) From the results of parts (e) and (f), evaluate the efficiency of the engine. A Stirling engine is easier to manufacture than an internal combustion engine or a turbine. It can run on burning garbage. It can run on the energy transferred by sunlight and produce no material exhaust. Stirling engines are not currently used in automobiles due to long startup times and poor acceleration response.

A firebox is at 750 K, and the ambient temperature is 300 K. The efficiency of a Carnot engine doing 150 J of work as it transports energy between these constanttemperature baths is 60.0%. The Carnot engine must take in energy 150 J/0.600 5 250 J from the hot reservoir and must put out 100 J of energy by heat into the environment. To follow Carnots reasoning, suppose some other heat engine S could have an efficiency of 70.0%. (a) Find the energy input and exhaust energy output of engine S as it does 150 J of work. (b) Let engine S operate as in part (a) and run the Carnot engine in reverse between the same reservoirs. The output work of engine S is the input work for the Carnot refrigerator. Find the total energy transferred to or from the firebox and the total energy transferred to or from the environment as both engines operate together. (c) Explain how the results of parts (a) and (b) show that the Clausius statement of the second law of thermodynamics is violated. (d) Find the energy input and work output of engine S as it puts out exhaust energy of 100 J. Let engine S operate as in part (c) and contribute 150 J of its work output to running the Carnot engine in reverse. Find (e) the total energy the firebox puts out as both engines operate together, (f) the total work output, and (g) the total energy transferred to the environment. (h) Explain how the results show that the KelvinPlanck statement of the second law is violated. Therefore, our assumption about the efficiency of engine S must be false. (i) Let the engines operate together through one cycle as in part (d). Find the change in entropy of the Universe. (j) Explain how the result of part (i) shows that the entropy statement of the second law is violated.

Review. This problem complements Problem 88 in Chapter 10. In the operation of a single-cylinder internal combustion piston engine, one charge of fuel explodes to drive the piston outward in the power stroke. Part of its energy output is stored in a turning flywheel. This energy is then used to push the piston inward to compress the next charge of fuel and air. In this compression process, assume an original volume of 0.120 L of a diatomic ideal gas at atmospheric pressure is compressed adiabatically to one-eighth of its original volume. (a) Find the work input required to compress the gas. (b) Assume the flywheel is a solid disk of mass 5.10 kg and radius 8.50 cm, turning freely without friction between the power stroke and the compression stroke. How fast must the flywheel turn immediately after the power stroke? This situation represents the minimum angular speed at which the engine can operate without stalling. (c) When the engines operation is well above the point of stalling, assume the flywheel puts 5.00% of its maximum energy into compressing the next charge of fuel and air. Find its maximum angular speed in this case.

A biology laboratory is maintained at a constant temperature of 7.00C by an air conditioner, which is vented to the air outside. On a typical hot summer day, the outside temperature is 27.0C and the air-conditioning unit emits energy to the outside at a rate of 10.0 kW. Model the unit as having a coefficient of performance (COP) equal to 40.0% of the COP of an ideal Carnot device. (a) At what rate does the air conditioner remove energy from the laboratory? (b) Calculate the power required for the work input. (c) Find the change in entropy of the Universe produced by the air conditioner in 1.00 h. (d) What If? The outside temperature increases to 32.0C. Find the fractional change in the COP of the air conditioner

A power plant, having a Carnot efficiency, produces 1.00 GW of electrical power from turbines that take in steam at 500 K and reject water at 300 K into a flowing river. The water downstream is 6.00 K warmer due to the output of the power plant. Determine the flow rate of the river.

A power plant, having a Carnot efficiency, produces electric power P from turbines that take in energy from steam at temperature Th and discharge energy at temperature Tc through a heat exchanger into a flowing river. The water downstream is warmer by DT due to the output of the power plant. Determine the flow rate of the river.

A 1.00-mol sample of an ideal monatomic gas is taken through the cycle shown in Figure P22.73. The process A S B is a reversible isothermal expansion. Calculate (a) the net work done by the gas, (b) the energy added to the gas by heat, (c) the energy exhausted from the gas by heat, and (d) the efficiency of the cycle. (e) Explain how the efficiency compares with that of a Carnot engine operating between the same temperature extremes.

A system consisting of n moles of an ideal gas with molar specific heat at constant pressure CP undergoes two reversible processes. It starts with pressure Pi and volume Vi , expands isothermally, and then contracts adiabatically to reach a final state with pressure Pi and volume 3Vi . (a) Find its change in entropy in the isothermal process. (The entropy does not change in the adiabatic process.) (b) What If? Explain why the answer to part (a) must be the same as the answer to Problem 77. (You do not need to solve Problem 77 to answer this question.)

A heat engine operates between two reservoirs at T2 5 600 K and T1 5 350 K. It takes in 1.00 3 103 J of energy from the higher-temperature reservoir and performs 250 J of work. Find (a) the entropy change of the Universe DSU for this process and (b) the work W that could have been done by an ideal Carnot engine operating between these two reservoirs. (c) Show that the difference between the amounts of work done in parts (a) and (b) is T1 DSU

A 1.00-mol sample of a monatomic ideal gas is taken through the cycle shown in Figure P22.76. At point A, the pressure, volume, and temperature are Pi , Vi , and Ti, respectively. In terms of R and Ti, find (a) the total energy entering the system by heat per cycle, (b) the total energy leaving the system by heat per cycle, and (c) the efficiency of an engine operating in this cycle. (d) Explain how the efficiency compares with that of an engine operating in a Carnot cycle between the same temperature extremes.

A sample consisting of n moles of an ideal gas undergoes a reversible isobaric expansion from volume Vi to volume 3Vi . Find the change in entropy of the gas by calculating ef i dQ /T, where dQ 5 nCP dT.

An athlete whose mass is 70.0 kg drinks 16.0 ounces (454 g) of refrigerated water. The water is at a temperature of 35.0F. (a) Ignoring the temperature change of the body that results from the water intake (so that the body is regarded as a reservoir always at 98.6F), find the entropy increase of the entire system. (b) What If? Assume the entire body is cooled by the drink and the average specific heat of a person is equal to the specific heat of liquid water. Ignoring any other energy transfers by heat and any metabolic energy release, find the athletes temperature after she drinks the cold water given an initial body temperature of 98.6F. (c) Under these assumptions, what is the entropy increase of the entire system? (d) State how this result compares with the one you obtained in part (a).

A sample of an ideal gas expands isothermally, doubling in volume. (a) Show that the work done on the gas in expanding is W 5 2nRT ln 2. (b) Because the internal energy E int of an ideal gas depends solely on its temperature, the change in internal energy is zero during the expansion. It follows from the first law that the energy input to the gas by heat during the expansion is equal to the energy output by work. Does this process have 100% efficiency in converting energy input by heat into work output? (c) Does this conversion violate the second law? Explain.

Why is the following situation impossible? Two samples of water are mixed at constant pressure inside an insulated container: 1.00 kg of water at 10.0C and 1.00 kg of water at 30.0C. Because the container is insulated, there is no exchange of energy by heat between the water and the environment. Furthermore, the amount of energy that leaves the warm water by heat is equal to the amount that enters the cool water by heat. Therefore, the entropy change of the Universe is zero for this process.

A 1.00-mol sample of an ideal gas (g 5 1.40) is carried through the Carnot cycle described in Figure 22.11. At point A, the pressure is 25.0 atm and the temperature is 600 K. At point C, the pressure is 1.00 atm and the temperature is 400 K. (a) Determine the pressures and volumes at points A, B, C, and D. (b) Calculate the net work done per cycle.

The compression ratio of an Otto cycle as shown in Figure 22.13 is VA/VB 5 8.00. At the beginning A of the compression process, 500 cm3 of gas is at 100 kPa and 20.0C. At the beginning of the adiabatic expansion, the temperature is TC 5 750C. Model the working fluid as an ideal gas with g 5 1.40. (a) Fill in this table to follow the states of the gas: T (K) P (kPa) V (cm3) A 293 100 500 B C 1 023 D (b) Fill in this table to follow the processes: Q W DEint A S B B S C C S D D S A ABCDA (c) Identify the energy input |Q h |, (d) the energy exhaust |Q c |, and (e) the net output work Weng. (f) Calculate the thermal efficiency. (g) Find the number of crankshaft revolutions per minute required for a onecylinder engine to have an output power of 1.00 kW 5 1.34 hp. Note: The thermodynamic cycle involves four piston strokes.