A heat engine with 20.0 percent efficiency does 0.100 kJ

ENGINEERING APPLICATION Modern automobile gasoline engines have efficiencies of about 25 percent. About what percentage of the heat of combustion is not used for work but released as heat? (a) 25%, (b) 50%, (c) 75%, (d) 100%, (e) You cannot tell from the data given.

If a heat engine does 100 kJ of work per cycle while releasing 400 kJ of heat, what is its efficiency? (a) 20%, (b) 25%, (c) 80%, (d) 400%, (e) You cannot tell from the data given.

If the heat absorbed by a heat engine is 600 kJ per cycle, and it releases 480 kJ of heat each cycle, what is its efficiency? (a) 20%, (b) 80%, (c) 100%, (d) You cannot tell from the data given.

Explain what distinguishes a refrigerator from a heat pump.

An air conditioners COP is mathematically identical to that of a refrigerator, that is, However a heat pumps COP is defined differently, as Explain clearly why the two COPs are defined differently. Hint: Think of the end use of the three different devices.

Explain why you cannot cool your kitchen by leaving your refrigerator door open on a hot day. (Why does turning on a room air conditioner cool down the room, but opening a refrigerator door does not?)

ENGINEERING APPLICATION Why do steam-power-plant designers try to increase the temperature of the steam as much as possible?

To increase the efficiency of a Carnot engine, you should (a) decrease the temperature of the hot reservoir, (b) increase the temperature of the cold reservoir, (c) increase the temperature of the hot reservoir, (d) change the ratio of maximum volume to minimum volume.

Explain why the following statement is true: To increase the efficiency of a Carnot engine, you should make the difference between the two operating temperatures as large as possible; but to increase the efficiency of a Carnot cycle refrigerator, you should make the difference between the two operating temperatures as small as possible.

A Carnot engine operates between a cold temperature reservoir of and a high temperature reservoir of Its efficiency is (a) 21%, (b) 25%, (c) 75%, (d) 79%.

The Carnot engine in Problem 10 is run in reverse as a refrigerator. Its COP is (a) 0.33, (b) 1.3, (c) 3.0, (d) 4.7.

On a humid day, water vapor condenses on a cold surface. During condensation, the entropy of the water (a) increases, (b) remains constant, (c) decreases, (d) may decrease or remain unchanged. Explain your answer.

An ideal gas is taken reversibly from an initial state to the final state Two possible paths are (A) an isothermal expansion followed by an adiabatic compression, and (B) an adiabatic compression followed by an isothermal expansion. For these two paths, (a) (b) (c) (d) None of the above.

Figure 19-12 shows a thermodynamic cycle for an ideal gas on an ST diagram. Identify this cycle and sketch it on a PV diagram.

Figure 19-13 shows a thermodynamic cycle for an ideal gas on an diagram. Identify the type of engine represented by this diagram.

Sketch an diagram of the Otto cycle. (The Otto cycle is discussed in Section 19-1.)

Sketch an diagram of the Carnot cycle for an ideal gas.

Sketch an diagram of the Otto cycle. (The Otto cycle is discussed in Section 19-1.)

Figure 19-14 shows a thermodynamic cycle for an ideal gas on an SP diagram. Make a sketch of this cycle on a PV diagram.

CONTEXT-RICH One afternoon, the mother of one of your friends walks into his room and finds a mess. She asks your friend how the room came to be in such a state, and your friend replies, Well, it is the natural destiny of any closed system to degenerate toward greater and greater levels of entropy. Thats all, Mom. Her reply is a sharp Nevertheless, youd better clean your room. Your friend retorts, But that cant happen. It would violate the second law of thermodynamics. Critique your friends response. Is his mother correct to ground him for not cleaning his room, or is cleaning the room really impossible?

Estimate the change in COP of your electric food freezer when it is removed from your kitchen to its new location in your basement, which is cooler than your kitchen.

Estimate the probability that all the molecules in your bedroom are located in the (open) closet which accounts for about 10 percent of the total volume of the room.

Estimate the maximum efficiency of an automobile engine that has a compression ratio of 8.0:1.0. Assume the engine operates according to the Otto cycle and assume \(\gamma=1.4\). (The Otto cycle is discussed in Section 19-1).

CONTEXT-RICH You are working as an appliance salesperson during the summer. One day, your physics professor comes into your store to buy a new refrigerator. Wanting to buy the most efficient refrigerator possible, she asks you about the efficiencies of the available models. She decides to return the next day to buy the most efficient refrigerator. To make the sale, you need to provide her with the following estimates: (a) the highest COP possible for a household refrigerator, and (b) the highest rate possible for the heat to be released by the interior of the refrigerator if the refrigerator uses 600 W of electrical power.

The average temperature of the surface of the Sun is about 5400 K, and the average temperature of the surface of Earth is about 290 K. The solar constant (the intensity of sunlight reaching Earths atmosphere) is about (a) Estimate the total power of the sunlight hitting Earth. (b) Estimate the net rate at which Earths entropy is increasing due to this solar radiation.

A1.0-L box contains molecules of an ideal gas, and the positions of the molecules are observed 100 times per second. Calculate the average time it should take before we observe all molecules in the left half of the box if is equal to (a) 10, (b) 100, (c) 1000, and (d) 1.0 mole. (e) The best vacuums that have been created to date have pressures of about If a vacuum chamber has the same volume as the box, how long will a physicist have to wait before all of the gas molecules in the vacuum chamber occupy only the left half of it? Compare that to the expected lifetime of the universe, which is about years.

A heat engine with 20.0 percent efficiency does 0.100 kJ of work during each cycle. (a) How much heat is absorbed from the hot reservoir during each cycle? (b) How much heat is released to the cold reservoir during each cycle?

A heat engine absorbs 0.400 kJ of heat and does 0.120 kJ of work during each cycle. (a) What is the engines efficiency? (b) How much heat is released to the cold reservoir during each cycle?

A heat engine absorbs 100 J of heat from the hot reservoir and releases 60 J of heat to the cold reservoir during each cycle. (a) What is its efficiency? (b) If each cycle takes 0.50 s, find the power output of this engine.

Arefrigerator absorbs 5.0 kJ of heat from a cold reservoir and releases 8.0 kJ to a hot reservoir. (a) Find the coefficient of performance of the refrigerator. (b) The refrigerator is reversible. If it is run backward as a heat engine between the same two reservoirs, what is its efficiency?

The working substance of heat an engine is 1.00 mol of a monatomic ideal gas. The cycle begins at and The gas is heated at constant volume to It then expands at constant pressure until it is The gas is then cooled at constant volume until its pressure is again 1.00 atm. It is then compressed at constant pressure to its original state. All the steps are quasi-static and reversible. (a) Show this cycle on a diagram. For each step of the cycle, find the work done by the gas, the heat absorbed by the gas, and the change in the internal energy of the gas. (b) Find the efficiency of the cycle.

The working substance of an engine is 1.00 mol of a diatomic ideal gas. The engine operates in a cycle consisting of three steps: (1) an adiabatic expansion from an initial volume of 10.0 L to a pressure of 1.00 atm and a volume of 20.0 L, (2) a compression at constant pressure to its original volume of 10.0 L, and (3) heating at constant volume to its original pressure. Find the efficiency of this cycle.

An engine using 1.00 mol of an ideal gas initially at a volume of and a temperature of performs a cycle consisting of four steps: (1) an isothermal expansion at a temperature of to twice its initial volume, (2) cooling at constant volume to a temperature of (3) an isothermal compression to its original volume, and (4) heating at constant volume to its original temperature of 400 K. Assume that . Sketch the cycle on a diagram and find its efficiency.

Figure 19-15 shows the cycle followed by 1.00 mol of an ideal monatomic gas at an initial volume All the processes are quasi-static. Determine (a) the temperature of each numbered state of the cycle, (b) the heat transfer for each part of the cycle, and (c) the efficiency of the cycle.

An ideal diatomic gas follows the cycle shown in Figure 19-16. The temperature of state 1 is 200 K. Determine (a) the temperatures of the other three numbered states of the cycle, and (b) the efficiency of the cycle.

ENGINEERING APPLICATION Recently, an old design for a heat engine, known as the Stirling engine, has been promoted as a means of producing power from solar energy. The cycle of a Stirling engine is as follows: (1) isothermal compression of the working gas, (2) heating of the gas at constant volume, (3) an isothermal expansion of the gas, and (4) cooling of the gas at constant volume. (a) Sketch and diagrams for the Stirling cycle. (b) Find the entropy change of the gas for each step of the cycle and show that the sum of these entropy changes is equal to zero.

BIOLOGICAL APPLICATION As far as we know, Nature has never evolved a heat engineSteven Vogel, Lifes Devices (Princeton University Press, 1988). (a) Calculate the efficiency of a heat engine operating between body temperature and a typical outdoor temperature and compare this to the human bodys efficiency for converting chemical energy into work (approximately 20 percent). Does this efficiency comparison contradict the second law of thermodynamics? (b) From the result of Part (a), and a general knowledge of the conditions under which most warm-blooded organisms exist, give a reason why no warmblooded organisms have evolved heat engines to increase their internal energies.

ENGINEERING APPLICATION The diesel cycle shown in Figure 19-17 approximates the behavior of a diesel engine. Process is an adiabatic compression, process is an expansion at constant pressure, process is an adiabatic expansion, and process is cooling at constant volume. Find the efficiency of this cycle in terms of the volumes and V

A refrigerator absorbs 500 J of heat from a cold reservoir and releases 800 J to a hot reservoir. Assume that the heat-engine statement of the second law of thermodynamics is false, and show how a perfect engine working with this refrigerator can violate the refrigerator statement of the second law of thermodynamics.

If two curves that represent quasi-static adiabatic processes could intersect on a diagram, a cycle could be completed by an isothermal path between the two adiabatic curves shown in Figure 19-18. Show that such a cycle violates the second law of thermodynamics.

A Carnot engine works between two heat reservoirs at temperatures and (a) What is its efficiency? (b) If it absorbs 100 J of heat from the hot reservoir during each cycle, how much work does it do each cycle? (c) How much heat does it release during each cycle? (d) What is the COP of this engine when it works as a refrigerator between the same two reservoirs? SSM

An engine absorbs 250 J of heat per cycle from a reservoir at 300 K and releases 200 J of heat per cycle to a reservoir at 200 K. (a) What is its efficiency? (b) How much additional work per cycle could be done if the engine were reversible?

A reversible engine working between two reservoirs at temperatures and has an efficiency of 30 percent. Working as a heat engine, it releases 140 J per cycle of heat to the cold reservoir. A second engine working between the same two reservoirs also releases 140 J per cycle to the cold reservoir. Show that if the second engine has an efficiency greater than 30 percent, the two engines working together would violate the heat-engine statement of the second law.

A reversible engine working between two reservoirs at temperatures and has an efficiency of 20 percent. Working as a heat engine, it does 100 J of work per cycle. A second engine working between the same two reservoirs also does 100 J of work per cycle. Show that if the efficiency of the second engine is greater than 20 percent, the two engines working together would violate the refrigerator statement of the second law.

A Carnot engine works between two heat reservoirs as a refrigerator. During each cycle, 100 J of heat are absorbed from the cold reservoir and 150 J of heat are released to the hot reservoir. (a) What is the efficiency of the Carnot engine when it works as a heat engine between the same two reservoirs? (b) Show that no other engine working as a refrigerator between the same two reservoirs can have a COP greater than 2.00.

A Carnot engine works between two heat reservoirs at temperatures and (a) What is its efficiency? (b) If it absorbs 100 J of heat from the hot reservoir during each cycle, how much work does it do? (c) How much heat does it release to the low-temperature reservoir during each cycle? (d) What is the coefficient of performance of this engine when it works as a refrigerator between these two reservoirs?

In the cycle shown in Figure 19-19, 1.00 mol of an ideal diatomic gas is initially at a pressure of 1.00 atm and a temperature of The gas is heated at constant volume to and is then expanded adiabatically until its pressure is again 1.00 atm. It is then compressed at constant pressure back to its original state. Find (a) the temperature after the adiabatic expansion, (b) the heat absorbed or released by the system during each step, (c) the efficiency of this cycle, and (d) the efficiency of a Carnot cycle operating between the temperature extremes of this cycle. SSM

ENGINEERING APPLICATION, CONTEXT-RICH You are a part of a team that is completing a mechanical engineering project. Your team built a steam engine that takes in superheated steam at and discharges condensed steam from its cylinder at Your team has measured the engines efficiency to be 30.0 percent. (a) How does this efficiency compare with the maximum possible efficiency for your engine? (b) If the useful power output of the engine is known to be 200 kW, how much heat does the engine release to its surroundings in 1.00 h?

ENGINEERING APPLICATION, CONTEXT-RICH As an engineer, you are designing a heat pump that is capable of delivering heat at the rate of 20 kW to a house. The house is located where, in January, the average outside temperature is The temperature of the air in the air handler inside the house is to be (a) What is the maximum possible COP for a heat pump operating between these temperatures? (b) What must the minimum power of the electric motor driving the heat pump be? (c) In reality, the COP of the heat pump will be only 60 percent of the ideal value. What is the minimum power of the electric motor when the COP is 60 percent of the ideal value?

Arefrigerator is rated at 370 W. (a) What is the maximum amount of heat it can absorb from the food compartment in 1.00 min if the food-compartment temperature of the refrigerator is and it releases heat into a room at ? (b) If the COP of the refrigerator is 70 percent of that of a reversible refrigerator, how much heat can it absorb from the food compartment in 1.00 min under these conditions?

A refrigerator is rated at 370 W. (a) What is the maximum amount of heat it can absorb from the food compartment in 1.00 min if the temperature in the compartment is and it releases heat into a room at ? (b) If the COP of the refrigerator is 70 percent of that of a reversible pump, how much heat can it absorb from the food compartment in 1.00 min? Is the COP for the refrigerator greater when the temperature of the room is or Explain.

CONTEXT-RICH You are installing a heat pump whose COP is half the COP of a reversible heat pump. You plan to use the pump on chilly winter nights to increase the air temperature in your bedroom. Your bedrooms dimensions are The air temperature should increase from to The outside temperature is and the temperature at the air handler in the room is If the pumps electric-power consumption is 750 W, how long will you have to wait for the rooms air to warm if the specific heat of air is Assume you have good window draperies and good wall insulation so that you can neglect the release of heat through windows, walls, ceilings, and floors. Also assume that the heat capacity of the floor, ceiling, walls, and furniture are negligible.

You inadvertently leave a pan of water boiling on the hot stove. You return just in time to see the last drop converted into steam. The pan originally held 1.00 L of boiling water. What is the change in entropy of the water associated with its change of state from liquid to gas? SSM

What is the change in entropy of 1.00 mol of liquid water at that freezes to ice at

Consider the freezing of 50.0 g of water once it is placed in the freezer compartment of a refrigerator. Assume the walls of the freezer are maintained at The water, initially liquid at 0. is frozen into ice and cooled to Show that even though the entropy of the water decreases, the net entropy of the universe increases.

In this problem, 2.00 mol of an ideal gas at 400 K expand quasi-statically and isothermally from an initial volume of 40.0 L to a final volume of 80.0 L. (a) What is the entropy change of the gas? (b) What is the entropy change of the universe for this process?

A system completes a cycle consisting of six quasi-static steps, during which the total work done by the system is 100 J. During step 1 the system absorbs 300 J of heat from a reservoir at 300 K, during step 3 the system absorbs 200 J of heat from a reservoir at 400 K, and during step 5 it absorbs heat from a reservoir at temperature . (During steps 2, 4 and 6 the system undergoes adiabatic processes in which the temperature of the system changes from one reservoir's temperature to that of the next.) (a) What is the entropy change of the system for the complete cycle? (b) If the cycle is reversible, what is the temperature

In this problem, 2.00 mol of an ideal gas initially has a temperature of 400 K and a volume of 40.0 L. The gas undergoes a free adiabatic expansion to twice its initial volume. What are (a) the entropy change of the gas, and (b) the entropy change of the universe?

A 200-kg block of ice at is placed in a large lake. The temperature of the lake is just slightly higher than and the ice melts very slowly. (a) What is the entropy change of the ice? (b) What is the entropy change of the lake? (c) What is the entropy change of the universe (the ice plus the lake)?

A 100-g piece of ice at is placed in an insulated calorimeter of negligible heat capacity containing 100 g of water at (a) What is the final temperature of the water once thermal equilibrium is established? (b) Find the entropy change of the universe for this process.

A 1.00-kg block of copper at is placed in an insulated calorimeter of negligible heat capacity containing 4.00 L of liquid water at Find the entropy change of (a) the copper block, (b) the water, and (c) the universe

If a 2.00-kg piece of lead at is dropped into a lake at find the entropy change of the universe.

A reservoir at 300 K absorbs 500 J of heat from a second reservoir at 400 K. (a) What is the change in entropy of the universe, and (b) how much work is lost during the process?

In this problem, 1.00 mol of an ideal gas at 300 K undergoes a free adiabatic expansion from to . It is then compressed isothermally and reversibly back to its original state. (a) What is the entropy change of the universe for the complete cycle? (b) How much work is lost in this cycle? (c) Show that the work lost is T Su

A heat engine with an output of 200 W has an efficiency of 30 percent. It operates at (a) How much work is done by the engine during each cycle? (b) How much heat is absorbed from the hot reservoir and how much is released to the cold reservoir during each cycle?

During each cycle, a heat engine operating between two heat reservoirs absorbs 150 J from the reservoir at and releases 125 J to the reservoir at (a) What is the efficiency of this engine? (b) What is the ratio of its efficiency to that of a Carnot engine working between the same reservoirs? (This ratio is called the second law efficiency.)

An engine absorbs 200 kJ of heat per cycle from a reservoir at 500 K and releases heat to a reservoir at 200 K. The engines efficiency is 85 percent of that of a Carnot engine working between the same reservoirs. (a) What is the efficiency of this engine? (b) How much work is done in each cycle? (c) How much heat is released to the low-temperature reservoir during each cycle?

Estimate the change in entropy of the universe associated with an Olympic diver diving into the water from the 10-m platform.

To maintain the temperature inside a house at the electric power consumption of the electric baseboard heaters is 30.0 kW on a day when the outside temperature is At what rate does this house contribute to the increase in the entropy of the universe?

ENGINEERING APPLICATION Calvin Cliffs Nuclear Power Plant, located on the Hobbes River, generates 1.00 GW of power. In this plant, liquid sodium circulates between the reactor core and a heat exchanger located in the superheated steam that drives the turbine. Heat is absorbed by the liquid sodium in the core, and released by the liquid sodium (and into the superheated steam) in the heat exchanger. The temperature of the superheated steam is 500 K. Heat is released into the river, and the water in the river flows by at a temperature of (a) What is the highest efficiency that this plant can have? (b) How much heat is released into the river every second? (c) How much heat must be released by the core to supply 1.00 GW of electrical power? (d) Assume that new environmental laws have been passed to preserve the unique wildlife of the river. Because of these laws, the plant is not allowed to heat the river by more than What is the minimum flow rate that the water in the Hobbes River must have?

ENGINEERING APPLICATION, CONTEXT-RICH An inventor comes to you to explain his new invention. It is a novel heat engine using water vapor as the working substance. He claims that the water vapor absorbs heat at does work at the rate of 125 W, and releases heat to the air at the rate of only 25.0 W, when the air temperature is (a) Explain to him why he cannot be correct. (b) After careful analysis of the data in his prospectus folder, you decide he has made an error in the measurement of his exhausted-heat value. What is the minimum rate of exhausting heat that would make you consider believing him?

The cycle represented in Figure 19-12 (next to Problem 19-14) is for 1.00 mol of an ideal monatomic gas. The temperatures at points A and B are 300 and 750 K, respectively. What is the efficiency of the cyclic process ABCDA?

(a) Which of these two processes is more wasteful of available work? (1) A block moving with 0.50 J of kinetic energy being slowed to rest by sliding (kinetic) friction when the temperature of the environment is 300 K, or (2) A reservoir at 400 K releasing 1.00 kJ of heat to a reservoir at 300 K? Explain your choice. Hint: How much of the 1.00 kJ of heat could be converted into work by an ideal cyclic process? (b) What is the change in entropy of the universe for each process?

Helium, a monatomic gas, is initially at a pressure of 16 atm, a volume of 1.0 L, and a temperature of 600 K. It is quasistatically expanded at constant temperature until its volume is 4.0 L, and is then quasi-statically compressed at constant pressure until its volume and temperature are such that a quasi-static adiabatic compression will return the gas to its original state. (a) Sketch this cycle on a diagram. (b) Find the volume and temperature after the compression at constant pressure. (c) Find the work done during each step of the cycle. (d) Find the efficiency of the cycle.

A heat engine that does the work of blowing up a balloon at a pressure of 1.00 atm absorbs 4.00 kJ from a reservoir at The volume of the balloon increases by 4.00 L, and heat is released to a reservoir at a temperature where If the efficiency of the heat engine is 50 percent of the efficiency of a Carnot engine working between the same two reservoirs, find the temperature

Show that the coefficient of performance of a Carnot engine run as a refrigerator is related to the efficiency of a Carnot engine operating between the same two temperatures by

A freezer has a temperature \(T_c=-23^{\circ} \mathrm{C}\). The air in the kitchen has a temperature \(T_{\mathrm{h}}=27^{\circ} \mathrm{C}\). The freezer is not perfectly insulated, and heat leaks through the walls of the freezer at a rate of \(50 \mathrm{~W}\). Find the power of the motor that is needed to maintain the temperature in the freezer.

In a heat engine, 2.00 mol of a diatomic gas are taken through the cycle ABCA, as shown in Figure 19-20. (The diagram is not drawn to scale.) At A the pressure and temperature are 5.00 atm and 600 K. The volume at B is twice the volume at A. The segment BC is an adiabatic expansion, and the segment CA is an isothermal compression. (a) What is the volume of the gas at A? (b) What are the volume and temperature of the gas at B? (c) What is the temperature of the gas at C? (d) What is the volume of the gas at C? (e) How much work is done by the gas in each of the three segments of the cycle? ( f ) How much heat is absorbed or released by the gas in each segment of this cycle?

In a heat engine, 2.00 mol of a diatomic gas are carried through the cycle ABCDA, shown in Figure 19-21. (The diagram is not drawn to scale.) The segment AB represents an isothermal expansion, and the segment BC is an adiabatic expansion. The pressure and temperature at A are 5.00 atm and 600 K. The volume at B is twice the volume at A. The pressure at D is 1.00 atm. (a) What is the pressure at B? (b) What is the temperature at C? (c) Find the total work done by the gas in one cycle.

In a heat engine, 2.00 mol of a monatomic gas are taken through the cycle ABCA, as shown in Figure 19-20. (The diagram is not drawn to scale.) At A the pressure and temperature are 5.00 atm and 600 K. The volume at B is twice the volume at A. The segment BC is an adiabatic expansion, and the segment CA is an isothermal compression. (a) What is the volume of the gas at A? (b) What are the volume and temperature of the gas at B? (c) What is the temperature of the gas at C? (d) What is the volume of the gas at C? (e) How much work is done by the gas in each of the three segments of the cycle? (f) How much heat is absorbed by the gas in each segment of the cycle?

In a heat engine, 2.00 mol of a monatomic gas are carried through the cycle ABCDA as shown in Figure 19-21. (The diagram is not drawn to scale.) The segment AB represents an isothermal expansion, and the segment BC is an adiabatic expansion. The pressure and temperature at A are 5.00 atm and 600 K. The volume at B is twice the volume at A. The pressure at D is 1.00 atm. (a) What is the pressure at B? (b) What is the temperature at C? (c) Find the total work done by the gas in one cycle.

Compare the efficiency of the Otto cycle to the efficiency of the Carnot cycle operating between the same maximum and minimum temperatures. (The Otto cycle is discussed in Section 191.)

ENGINEERING APPLICATION Acommon practical cycle, often used in refrigeration, is the Brayton cycle, which involves (1) an adiabatic compression, (2) an isobaric (constant pressure) expansion, (3) an adiabatic expansion, and (4) an isobaric compression back to the original state. Assume the system begins the adiabatic compression at temperature and transitions to temperatures and after each leg of the cycle. (a) Sketch this cycle on a diagram. (b) Show that the efficiency of the overall cycle is given by (c) Show that this efficiency, can be written as where is the pressure ratio Phigh/Plow (the ratio of the maximum and minimum pressures in the cycle).

ENGINEERING APPLICATION Suppose the Brayton cycle engine (see Problem 83) is run in reverse as a refrigerator in your kitchen. In this case, the cycle begins at temperature and expands at constant pressure until its temperature is Then the gas is adiabatically compressed until its temperature is And then it is compressed at constant pressure, until its temperature is Finally, it adiabatically expands until it returns to its initial state at temperature (a) Sketch this cycle on a diagram. (b) Show that the coefficient of performance, is (c) Suppose your Brayton cycle refrigerator is run as follows. The cylinder containing the refrigerant (a monatomic gas) has an initial volume and pressure of 60 mL and 1.0 atm. After the expansion at constant pressure, the volume and temperature are 75 mL and The pressure ratio for the cycle is 5.0. What is the coefficient of performance for your refrigerator? (d) In order to absorb heat from the food compartment at the rate of 120 W, what is the rate at which electrical energy must be supplied to the motor of this refrigerator? (e) Assuming the refrigerator motor is actually running for only 4.0 h each day, how much does it add to your monthly electric bill. Assume 15 cents per kWh of electric energy and 30 days in a month.

Using (Equation 19-16) for the entropy change of an ideal gas, show explicitly that the entropy change is zero for a quasi-static adiabatic expansion from state to state

(a) Show that if the refrigerator statement of the second law of thermodynamics were not true, then the entropy of the universe could decrease. (b) Show that if the heat-engine statement of the second law were not true, then the entropy of the universe could decrease. (c) A third statement of the second law is that the entropy of the universe cannot decrease. Have you just proved that this statement is equivalent to the refrigerator and heat-engine statements?

Suppose that two heat engines are connected in series, such that the heat released by the first engine is used as the heat absorbed by the second engine, as shown in Figure 19-22. The efficiencies of the engines are and respectively. Show that the net efficiency of the combination is given by enet _ e1 _ e2 _ e1e2

Suppose that two heat engines are connected in series, such that the heat released by the first engine is used as the heat absorbed by the second engine, as shown in Figure 19-22. Suppose that each engine is an ideal reversible heat engine. Engine 1 operates between temperatures and and Engine 2 operates between and where Show that the net efficiency of the combination is given by (Note that this result means that two reversible heat engines operating in series are equivalent to one reversible heat engine operating between the hottest and coldest reservoirs.)

The English mathematician and philospher Bertrand Russell (18721970) once said that if a million monkeys were given a million typewriters and typed away at random for a million years, they would produce all of Shakespeares works. Let us limit ourselves to the following fragment of Shakespeare (Julius Caesar III:ii): Friends, Romans, countrymen Lend me your ears. I come to bury Caesar, not to praise him. The evil that men do lives on after them, The good is oft interred with the bones. So let it be with Caesar. The noble Brutus hath told you that Caesar was ambitious, And, if so, it were a grievous fault, And grievously hath Caesar answered it... Even with this small fragment, it will take a lot longer than a million years! By what factor (roughly speaking) was Russell in error? Make any reasonable assumptions you want. (You can even assume that the monkeys are immortal.) SSM