The pressure and volume of an ideal monatomic gas change

In moving out of a dormitory at the end of the semester, a student does 1.6 3 104 J of work. In the process, his internal energy decreases by 4.2 3 104 J. Determine each of the following quantities (including the algebraic sign): (a) W (b) DU (c) Q

The internal energy of a system changes because the system gains 165 J of heat and performs 312 J of work. In returning to its initial state, the system loses 114 J of heat. During this return process, (a) what work is involved, and (b) is the work done by the system or on the system?

A system does 164 J of work on its environment and gains 77 J of heat in the process. Find the change in the internal energy of (a) the system and (b) the environment.

A system does 4.8 3 104 J of work, and 7.6 3 104 J of heat fl ows into the system during the process. Find the change in the internal energy of the system.

In a game of football outdoors on a cold day, a player will begin to feel exhausted after using approximately 8.0 3 105 J of internal energy. (a) One player, dressed too lightly for the weather, has to leave the game after losing 6.8 3 105 J of heat. How much work has he done? (b) Another player, wearing clothes that off er better protection against heat loss, is able to remain in the game long enough to do 2.1 3 105 J of work. What is the magnitude of the heat that he has lost?

Three moles of an ideal monatomic gas are at a temperature of 345 K. Then, 2438 J of heat is added to the gas, and 962 J of work is done on it. What is the fi nal temperature of the gas?

In exercising, a weight lifter loses 0.150 kg of water through evaporation, the heat required to evaporate the water coming from the weight lifters body. The work done in lifting weights is 1.40 3 105 J. (a) Assuming that the latent heat of vaporization of perspiration is 2.42 3 106 J/kg, fi nd the change in the internal energy of the weight lifter. (b) Determine the minimum number of nutritional Calories of food (1 nutritional Calorie 5 4186 J) that must be consumed to replace the loss of internal energy

A system undergoes a two-step process. In the fi rst step, the internal energy of the system increases by 228 J when 166 J of work is done on the system. In the second step, the internal energy of the system increases by 115 J when 177 J of work is done on the system. For the overall process, fi nd the heat. What type of process is the overall process? Explain.

When a .22-caliber rifl e is fi red, the expanding gas from the burning gunpowder creates a pressure behind the bullet. This pressure causes the force that pushes the bullet through the barrel. The barrel has a length of 0.61 m and an opening whose radius is 2.8 3 1023 m. A bullet (mass 5 2.6 3 1023 kg) has a speed of 370 m/s after passing through this barrel. Ignore friction and determine the average pressure of the expanding gas

A system gains 2780 J of heat at a constant pressure of 1.26 3 105 Pa, and its internal energy increases by 3990 J. What is the change in the volume of the system, and is it an increase or a decrease?

A system gains 1500 J of heat, while the internal energy of the system increases by 4500 J and the volume decreases by 0.010 m3 . Assume that the pressure is constant and fi nd its value.

The volume of a gas is changed along the curved line between A and B in the drawing. Do not assume that the curved line is an isotherm or that the gas is ideal. (a) Find the magnitude of the work for the process, and (b) determine whether the work is positive or negative.

Using the data presented in the accompanying pressure volume graph, estimate the magnitude of the work done when the system changes from A to B to C along the path shown. (b) Determine whether the work is done by the system or on the system and, hence, whether the work is positive or negative.

Sections 14.2 and 14.3 provide useful information for this problem. When a monatomic ideal gas expands at a constant pressure of 2.6 3 105 Pa, the volume of the gas increases by 6.2 3 1023 m3 . (a) Determine the heat that fl ows into or out of the gas. (b) Specify the direction of the fl ow

A gas is contained in a chamber such as that in Figure 15.4. Suppose that the region outside the chamber is evacuated and the total mass of the block and the movable piston is 135 kg. When 2050 J of heat fl ows into the gas, the internal energy of the gas increases by 1730 J. What is the distance s through which the piston rises?

A piece of aluminum has a volume of 1.4 3 1023 m3 . The coeffi - cient of volume expansion for aluminum is b 5 69 3 1026 (C8)21 . The temperature of this object is raised from 20 to 320 8C. How much work is done by the expanding aluminum if the air pressure is 1.01 3 105 Pa?

Refer to Multiple-Concept Example 3 to see how the concepts pertinent to this problem are used. The pressure of a gas remains constant while the temperature, volume, and internal energy of the gas increase by 53.0 C8, 1.40 3 1023 m3 , and 939 J, respectively. The mass of the gas is 24.0 g, and its specifi c heat capacity is 1080 J/(kg ? C8). Determine the pressure.

Refer to the drawing that accompanies Problem 13. When a system changes from A to B along the path shown on the pressure-versus-volume graph, it gains 2700 J of heat. What is the change in the internal energy of the system?

Water is heated in an open pan where the air pressure is one atmosphere. The water remains a liquid, which expands by a small amount as it is heated. Determine the ratio of the work done by the water to the heat absorbed by the water

Six grams of helium (molecular mass 5 4.0 u) expand isothermally at 370 K and does 9600 J of work. Assuming that helium is an ideal gas, determine the ratio of the fi nal volume of the gas to the initial volume

Five moles of a monatomic ideal gas expand adiabatically, and its temperature decreases from 370 to 290 K. Determine (a) the work done (including the algebraic sign) by the gas, and (b) the change in its internal energy.

Three moles of neon expand isothermally to 0.250 from 0.100 m3 . Into the gas fl ows 4.75 3 103 J of heat. Assuming that neon is an ideal gas, fi nd its temperature.

The temperature of a monatomic ideal gas remains constant during a process in which 4700 J of heat fl ows out of the gas. How much work (including the proper 1 or 2 sign) is done?

One-half mole of a monatomic ideal gas expands adiabatically and does 610 J of work. By how many kelvins does its temperature change? Specify whether the change is an increase or a decrease.

A monatomic ideal gas has an initial temperature of 405 K. This gas expands and does the same amount of work whether the expansion is adiabatic or isothermal. When the expansion is adiabatic, the fi nal temperature of the gas is 245 K. What is the ratio of the fi nal to the initial volume when the expansion is isothermal?

Heat is added isothermally to 2.5 mol of a monatomic ideal gas. The temperature of the gas is 430 K. How much heat must be added to make the volume of the gas double?

A diesel engine does not use spark plugs to ignite the fuel and air in the cylinders. Instead, the temperature required to ignite the fuel occurs because the pistons compress the air in the cylinders. Suppose that air at an initial temperature of 21 8C is compressed adiabatically to a temperature of 688 8C. Assume the air to be an ideal gas for which g 5 7 5. Find the compression ratio, which is the ratio of the initial volume to the fi nal volume

A monatomic ideal gas expands from point A to point B along the path shown in the drawing. (a) Determine the work done by the gas. (b) The temperature of the gas at point A is 185 K. What is its temperature at point B? (c) How much heat has been added to or removed from the gas during the process?

The drawing refers to one mole of a monatomic ideal gas and shows a process that has four steps, two isobaric (A to B, C to D) and two isochoric (B to C, D to A). Complete the following table by calculating DU, W, and Q (including the algebraic signs) for each of the four steps.

A monatomic ideal gas (g 5 5 3 ) is contained within a perfectly insulated cylinder that is fi tted with a movable piston. The initial pressure of the gas is 1.50 3 105 Pa. The piston is pushed so as to compress the gas, with the result that the Kelvin temperature doubles. What is the fi nal pressure of the gas?

The pressure and volume of an ideal monatomic gas change from A to B to C, as the drawing shows. The curved line between A and C is an isotherm. (a) Determine the total heat for the process and (b) state whether the fl ow of heat is into or out of the gas.

The work done by one mole of a monatomic ideal gas (g 5 5 3 ) in expanding adiabatically is 825 J. The initial temperature and volume of the gas are 393 K and 0.100 m3 . Obtain (a) the fi nal temperature and (b) the fi nal volume of the gas.

The drawing shows an adiabatically isolated cylinder that is divided initially into two identical parts by an adiabatic partition. Both sides contain one mole of a monatomic ideal gas (g 5 5 3 ), with the initial temperature being 525 K on the left and 275 K on the right. The partition is then allowed to move slowly (i.e., quasi-statically) to the right, until the pressures on each side of the partition are the same. Find the fi nal temperatures on the (a) left and (b) right.

Argon is a monatomic gas whose atomic mass is 39.9 u. The temperature of eight grams of argon is raised by 75 K under conditions of constant pressure. Assuming that argon behaves as an ideal gas, how much heat is required?

The temperature of 2.5 mol of a monatomic ideal gas is 350 K. The internal energy of this gas is doubled by the addition of heat. How much heat is needed when it is added at (a) constant volume and (b) constant pressure?

Under constant-volume conditions, 3500 J of heat is added to 1.6 moles of an ideal gas. As a result, the temperature of the gas increases by 75 K. How much heat would be required to cause the same temperature change under constant-pressure conditions? Do not assume anything about whether the gas is monatomic, diatomic, etc.

Heat is added to two identical samples of a monatomic ideal gas. In the fi rst sample the heat is added while the volume of the gas is kept constant, and the heat causes the temperature to rise by 75 K. In the second sample, an identical amount of heat is added while the pressure (but not the volume) of the gas is kept constant. By how much does the temperature of this sample increase?

A monatomic ideal gas in a rigid container is heated from 217 K to 279 K by adding 8500 J of heat. How many moles of gas are there in the container?

Three moles of a monatomic ideal gas are heated at a constant volume of 1.50 m3 . The amount of heat added is 5.24 3 103 J. (a) What is the change in the temperature of the gas? (b) Find the change in its internal energy. (c) Determine the change in pressure.

A monatomic ideal gas expands at constant pressure. (a) What percentage of the heat being supplied to the gas is used to increase the internal energy of the gas? (b) What percentage is used for doing the work of expansion?

Suppose a monatomic ideal gas is contained within a vertical cylinder that is fi tted with a movable piston. The piston is frictionless and has a negligible mass. The area of the piston is 3.14 3 1022 m2 , and the pressure outside the cylinder is 1.01 3 105 Pa. Heat (2093 J) is removed from the gas. Through what distance does the piston drop?

A monatomic ideal gas is heated while at a constant volume of 1.00 3 1023 m3 , using a ten-watt heater. The pressure of the gas increases by 5.0 3 104 Pa. How long was the heater on?

One mole of neon, a monatomic gas, starts out at conditions of standard temperature and pressure. The gas is heated at constant volume until its pressure is tripled, then further heated at constant pressure until its volume is doubled. Assume that neon behaves as an ideal gas. For the entire process, fi nd the heat added to the gas.

Multiple-Concept Example 6 provides a review of the concepts that play roles here. An engine has an effi ciency of 64% and produces 5500 J of work. Determine (a) the input heat and (b) the rejected heat

Heat engines take input energy in the form of heat, use some of that energy to do work, and exhaust the remainder. Similarly, a person can be viewed as a heat engine that takes an input of internal energy, uses some of it to do work, and gives off the rest as heat. Suppose that a trained athlete can function as a heat engine with an effi ciency of 0.11. (a) What is the magnitude of the internal energy that the athlete uses in order to do 5.1 3 104 J of work? (b) Determine the magnitude of the heat the athlete gives off .

Engine 1 has an effi ciency of 0.18 and requires 5500 J of input heat to perform a certain amount of work. Engine 2 has an effi ciency of 0.26 and performs the same amount of work. How much input heat does the second engine require?

Due to a tune-up, the effi ciency of an automobile engine increases by 5.0%. For an input heat of 1300 J, how much more work does the engine produce after the tune-up than before?

A 52-kg mountain climber, starting from rest, climbs a vertical distance of 730 m. At the top, she is again at rest. In the process, her body generates 4.1 3 106 J of energy via metabolic processes. In fact, her body acts like a heat engine, the effi ciency of which is given by Equation 15.11 as e 5 uWu/uQHu, where uWu is the magnitude of the work she does and uQHu is the magnitude of the input heat. Find her effi ciency as a heat engine.

Due to design changes, the effi ciency of an engine increases from 0.23 to 0.42. For the same input heat uQHu, these changes increase the work done by the more effi cient engine and reduce the amount of heat rejected to the cold reservoir. Find the ratio of the heat rejected to the cold reservoir for the improved engine to that for the original engine.

Engine A receives three times more input heat, produces fi ve times more work, and rejects two times more heat than engine B. Find the effi - ciency of (a) engine A and (b) engine B.

A Carnot engine operates with an effi ciency of 27.0% when the temperature of its cold reservoir is 275 K. Assuming that the temperature of the hot reservoir remains the same, what must be the temperature of the cold reservoir in order to increase the effi ciency to 32.0%?

An engine has a hot-reservoir temperature of 950 K and a cold-reservoir temperature of 620 K. The engine operates at three-fi fths maximum effi - ciency. What is the effi ciency of the engine?

A Carnot engine has an effi ciency of 0.700, and the temperature of its cold reservoir is 378 K. (a) Determine the temperature of its hot reservoir. (b) If 5230 J of heat is rejected to the cold reservoir, what amount of heat is put into the engine?

A Carnot engine operates with a large hot reservoir and a much smaller cold reservoir. As a result, the temperature of the hot reservoir remains constant while the temperature of the cold reservoir slowly increases. This temperature change decreases the effi ciency of the engine to 0.70 from 0.75. Find the ratio of the fi nal temperature of the cold reservoir to its initial temperature.

An engine does 18 500 J of work and rejects 6550 J of heat into a cold reservoir whose temperature is 285 K. What would be the smallest possible temperature of the hot reservoir?

A Carnot engine has an effi ciency of 0.40. The Kelvin temperature of its hot reservoir is quadrupled, and the Kelvin temperature of its cold reservoir is doubled. What is the effi ciency that results from these changes?

A Carnot engine operates between temperatures of 650 and 350 K. To improve the effi ciency of the engine, it is decided either to raise the temperature of the hot reservoir by 40 K or to lower the temperature of the cold reservoir by 40 K. Which change gives the greater improvement? Justify your answer by calculating the effi ciency in each case

The hot reservoir for a Carnot engine has a temperature of 890 K, while the cold reservoir has a temperature of 670 K. The heat input for this engine is 4800 J. The 670-K reservoir also serves as the hot reservoir for a second Carnot engine. This second engine uses the rejected heat of the fi rst engine as input and extracts additional work from it. The rejected heat from the second engine goes into a reservoir that has a temperature of 420 K. Find the total work delivered by the two engines.

Suppose that the gasoline in a car engine burns at 631 8C, while the exhaust temperature (the temperature of the cold reservoir) is 139 8C and the outdoor temperature is 27 8C. Assume that the engine can be treated as a Carnot engine (a gross oversimplifi cation). In an attempt to increase mileage performance, an inventor builds a second engine that functions between the exhaust and outdoor temperatures and uses the exhaust heat to produce additional work. Assume that the inventors engine can also be treated as a Carnot engine. Determine the ratio of the total work produced by both engines to that produced by the fi rst engine alone.

A power plant taps steam superheated by geothermal energy to 505 K (the temperature of the hot reservoir) and uses the steam to do work in turning the turbine of an electric generator. The steam is then converted back into water in a condenser at 323 K (the temperature of the cold reservoir), after which the water is pumped back down into the earth where it is heated again. The output power (work per unit time) of the plant is 84 000 kilowatts. Determine (a) the maximum effi ciency at which this plant can operate and (b) the minimum amount of rejected heat that must be removed from the condenser every twenty-four hours.

The drawing (not to scale) shows the way in which the pressure and volume change for an ideal gas that is used as the working substance in a Carnot engine. The gas begins at point a (pressure 5 Pa, volume 5 Va) and expands isothermally at temperature TH until point b (pressure 5 Pb, volume 5 Vb) is reached. During this expansion, the input heat of magnitude uQHu enters the gas from the hot reservoir of the engine. Then, from point b to point c (pressure 5 Pc, volume 5 Vc), the gas expands adiabatically. Next, the gas is compressed isothermally at temperature TC from point c to point d (pressure 5 Pd, volume 5 Vd). During this compression, heat of magnitude uQCu is rejected to the cold reservoir of the engine. Finally, the gas is compressed adiabatically from point d to point a, where the gas is back in its initial state. The overall process a to b to c to d to a is called a Carnot cycle. Prove for this cycle that uQCu/uQHu 5 TC/TH.

reactor. In this type of reactor, nuclear energy causes water under pressure to boil at 285 8C (the temperature of the hot reservoir). After the steam does the work of turning the turbine of an electric generator, the steam is converted back into water in a condenser at 40 8C (the temperature of the cold reservoir). To keep the condenser at 40 8C, the rejected heat must be carried away by some meansfor example, by water from a river. The plant operates at three-fourths of its Carnot effi ciency, and the electrical output power of the plant is 1.2 3 109 watts. A river with a water fl ow rate of 1.0 3 105 kg/s is available to remove the rejected heat from the plant. Find the number of Celsius degrees by which the temperature of the river rises.

A Carnot air conditioner maintains the temperature in a house at 297 K on a day when the temperature outside is 311 K. What is the coeffi cient of performance of the air conditioner?

The inside of a Carnot refrigerator is maintained at a temperature of 277 K, while the temperature in the kitchen is 299 K. Using 2500 J of work, how much heat can this refrigerator remove from its inside compartment?

A refrigerator operates between temperatures of 296 and 275 K. What would be its maximum coeffi cient of performance?

Two Carnot air conditioners, A and B, are removing heat from diff erent rooms. The outside temperature is the same for both rooms, 309.0 K. The room serviced by unit A is kept at a temperature of 294.0 K, while the room serviced by unit B is kept at 301.0 K. The heat removed from either room is 4330 J. For both units, fi nd the magnitude of the work required and the magnitude of the heat deposited outside.

The water in a deep underground well is used as the cold reservoir of a Carnot heat pump that maintains the temperature of a house at 301 K. To deposit 14 200 J of heat in the house, the heat pump requires 800 J of work. Determine the temperature of the well water

A Carnot engine has an effi ciency of 0.55. If this engine were run backward as a heat pump, what would be the coeffi cient of performance?

A Carnot refrigerator is used in a kitchen in which the temperature is kept at 301 K. This refrigerator uses 241 J of work to remove 2561 J of heat from the food inside. What is the temperature inside the refrigerator?

The wattage of a commercial ice maker is 225 W and is the rate at which it does work. The ice maker operates just like a refrigerator or an air conditioner and has a coeffi cient of performance of 3.60. The water going into the unit has a temperature of 15.0 8C, and the ice maker produces ice cubes at 0.0 8C. Ignoring the work needed to keep stored ice from melting, fi nd the maximum amount (in kg) of ice that the unit can produce in one day of continuous operation.

Review Conceptual Example 9 before attempting this problem. A window air conditioner has an average coeffi cient of performance of 2.0. In a futile attempt to cool a bedroom, this unit has been placed on the fl oor by the bed. During this attempt, 7.6 3 104 J of heat is removed from the air in the front of the unit. Determine the net heat added to the room by operating the air conditioner in this manner.

How long would a 3.00-kW space heater have to run to put into a kitchen the same amount of heat as a refrigerator (coeffi cient of performance 5 3.00) does when it freezes 1.50 kg of water at 20.0 8C into ice at 0.0 8C?

A Carnot refrigerator transfers heat from its inside (6.0 C) to the room air outside (20.0 8C). (a) Find the coeffi cient of performance of the refrigerator. (b) Determine the magnitude of the minimum work needed to cool 5.00 kg of water from 20.0 to 6.0 8C when it is placed in the refrigerator.

A Carnot engine uses hot and cold reservoirs that have temperatures of 1684 and 842 K, respectively. The input heat for this engine is uQHu. The work delivered by the engine is used to operate a Carnot heat pump. The pump removes heat from the 842-K reservoir and puts it into a hot reservoir at a temperature T9. The amount of heat removed from the 842-K reservoir is also uQHu. Find the temperature T9.

Consider three engines that each use 1650 J of heat from a hot reservoir (temperature 5 550 K). These three engines reject heat to a cold reservoir (temperature 5 330 K). Engine I rejects 1120 J of heat. Engine II rejects 990 J of heat. Engine III rejects 660 J of heat. One of the engines operates reversibly, and two operate irreversibly. However, of the two irreversible engines, one violates the second law of thermodynamics and could not exist. For each of the engines determine the total entropy * * * * ** change of the universe, which is the sum of the entropy changes of the hot and cold reservoirs. On the basis of your calculations, identify which engine operates reversibly, which operates irreversibly and could exist, and which operates irreversibly and could not exist.

Heat Q fl ows spontaneously from a reservoir at 394 K into a reservoir at 298 K. Because of the spontaneous fl ow, 2800 J of energy is rendered unavailable for work when a Carnot engine operates between the reservoir at 298 K and a reservoir at 248 K. Find Q.

Find the change in entropy of the H2O molecules when (a) three kilograms of ice melts into water at 273 K and (b) three kilograms of water changes into steam at 373 K. (c) On the basis of the answers to parts (a) and (b), discuss which change creates more disorder in the collection of H2O molecules.

On a cold day, 24 500 J of heat leaks out of a house. The inside temperature is 21 8C, and the outside temperature is 215 8C. What is the increase in the entropy of the universe that this heat loss produces?

After 6.00 kg of water at 85.0 8C is mixed in a perfect thermos with 3.00 kg of ice at 0.0 8C, the mixture is allowed to reach equilibrium. When heat is added to or removed from a solid or liquid of mass m and specifi c heat capacity c, the change in entropy can be shown to be DS 5 mc ln(Tf/Ti), where Ti and Tf are the initial and fi nal Kelvin temperatures. Using this expression and the change in entropy for melting, fi nd the change in entropy that occurs. (b) Should the entropy of the universe increase or decrease as a result of the mixing process? Give your reasoning and state whether your answer in part (a) is consistent with your answer here.

The sun is a sphere with a radius of 6.96 3 108 m and an average surface temperature of 5800 K. Determine the amount by which the suns thermal radiation increases the entropy of the entire universe each second. Assume that the sun is a perfect blackbody, and that the average temperature of the rest of the universe is 2.73 K. Do not consider the thermal radiation absorbed by the sun from the rest of the universe

An irreversible engine operates between temperatures of 852 and 314 K. It absorbs 1285 J of heat from the hot reservoir and does 264 J of work. (a) What is the change DSuniverse in the entropy of the universe associated with the operation of this engine? (b) If the engine were reversible, what would be the magnitude uWu of the work it would have done, assuming that it operated between the same temperatures and absorbed the same heat as the irreversible engine? (c) Using the results of parts (a) and (b), fi nd the diff erence between the work produced by the reversible and irreversible engines.

The pressure of a monatomic ideal gas (g 5 5 3 ) doubles during an adiabatic compression. What is the ratio of the fi nal volume to the initial volume?

One-half mole of a monatomic ideal gas absorbs 1200 J of heat while 2500 J of work is done by the gas. (a) What is the temperature change of the gas? (b) Is the change an increase or a decrease?

Multiple-Concept Example 6 deals with the same concepts as this problem does. What is the effi ciency of a heat engine that uses an input heat of 5.6 3 104 J and rejects 1.8 3 104 J of heat?

A gas, while expanding under isobaric conditions, does 480 J of work. The pressure of the gas is 1.6 3 105 Pa, and its initial volume is 1.5 3 1023 m3 . What is the fi nal volume of the gas?

A lawnmower engine with an effi ciency of 0.22 rejects 9900 J of heat every second. What is the magnitude of the work that the engine does in one second?

A process occurs in which the entropy of a system increases by 125 J/K. During the process, the energy that becomes unavailable for doing work is zero. (a) Is this process reversible or irreversible? Give your reasoning. (b) Determine the change in the entropy of the surroundings.

A Carnot heat pump operates between an outdoor temperature of 265 K and an indoor temperature of 298 K. Find its coeffi cient of performance.

The temperatures indoors and outdoors are 299 and 312 K, respectively. A Carnot air conditioner deposits 6.12 3 105 J of heat outdoors. How much heat is removed from the house?

Carnot engine A has an effi ciency of 0.60, and Carnot engine B has an effi ciency of 0.80. Both engines utilize the same hot reservoir, which has a temperature of 650 K and delivers 1200 J of heat to each engine. Find the magnitude of the work produced by each engine and the temperatures of the cold reservoirs that they use

The pressure and volume of a gas are changed along the path ABCA. Using the data shown in the graph, determine the work done (including the algebraic sign) in each segment of the path: (a) A to B, (b) B to C, and (c) C to A

Refer to the drawing in Problem 12, where the curve between A and B is now an isotherm. An ideal gas begins at A and is changed along the horizontal line from A to C and then along the vertical line from C to B. (a) Find the heat for the process ACB and (b) determine whether it fl ows into or out of the gas.

Suppose that 31.4 J of heat is added to an ideal gas. The gas expands at a constant pressure of 1.40 3 104 Pa while changing its volume from 3.00 3 1024 to 8.00 3 1024 m3 . The gas is not monatomic, so the relation CP 5 5 2 R does not apply. (a) Determine the change in the internal energy of the gas. (b) Calculate its molar specifi c heat capacity CP.

An air conditioner keeps the inside of a house at a temperature of 19.0 8C when the outdoor temperature is 33.0 8C. Heat, leaking into the house at the rate of 10 500 joules per second, is removed by the air conditioner. Assuming that the air conditioner is a Carnot air conditioner, what is the work per second that must be done by the electrical energy in order to keep the inside temperature constant?

Even at rest, the human body generates heat. The heat arises because of the bodys metabolismthat is, the chemical reactions that are always occurring in the body to generate energy. In rooms designed for use by large groups, adequate ventilation or air conditioning must be provided to remove this heat. Consider a classroom containing 200 students. Assume that the metabolic rate of generating heat is 130 W for each student and that the heat accumulates during a fi fty-minute lecture. In addition, assume that the air has a molar specifi c heat of CV 5 5 2 R and that the room (volume 5 1200 m3 , initial pressure 5 1.01 3 105 Pa, and initial temperature 5 21 C) is sealed shut. If all the heat generated by the students were absorbed by the air, by how much would the air temperature rise during a lecture?

Heat fl ows from a reservoir at 373 K to a reservoir at 273 K through a 0.35-m copper rod with a cross-sectional area of 9.4 3 1024 m2 (see the drawing). The heat then leaves the 273-K reservoir and enters a Carnot engine, which uses part of this heat to do work and rejects the remainder to a third reservoir at 173 K. How much of the heat leaving the 373-K reservoir is rendered unavailable for doing work in a period of 2.0 min?

A fi fteen-watt heater is used to heat a monatomic ideal gas at a constant pressure of 7.60 3 105 Pa. During the process, the 1.40 3 1023 m3 volume of the gas increases by 25.0%. How long was the heater on?

An ideal gas is taken through the three processes (A B B, B B C, and C B A) shown in the drawing. In general, for each process the internal energy U of the gas can change because heat Q can be added to or removed from the gas and work W can be done by the gas or on the gas. For the three processes shown in the drawing, fi ll in the fi ve missing entries in the following table.

An engine has an effi ciency e1. The engine takes input heat of magnitude uQHu from a hot reservoir and delivers work of magnitude uW1u. The heat rejected by this engine is used as input heat for a second engine, which has an effi ciency e2 and delivers work of magnitude uW2u. The overall effi ciency of this two-engine device is the magnitude of the total work delivered (uW1u 1 uW2u) divided by the magnitude uQHu of the input heat. Find an expression for the overall effi ciency e in terms of e1 and e2.

Beginning with a pressure of 2.20 3 105 Pa and a volume of 6.34 3 1023 m3 , an ideal monatomic gas (g 5 5 3 ) undergoes an adiabatic expansion such that its fi nal pressure is 8.15 3 104 Pa. An alternative process leading to the same final state begins with an isochoric cooling to the final pressure, followed by an isobaric expansion to the final volume. How much more work does the gas do in the adiabatic process than in the alternative process?

An ideal, or Carnot, heat pump is used to heat a house to a temperature of 294 K (21 8C). How much work must the pump do to deliver 3350 J of the heat into the house on a day when the outdoor temperature is 273 K (0 8C), and on another day when the temperature is 252 K (221 8C)?

The sublimation of zinc (mass per mole 5 0.0654 kg/mol) takes place at a temperature of 6.00 3 102 K, and the latent heat of sublimation is 1.99 3 106 J/kg. The pressure remains constant during the sublimation. Assume that the zinc vapor can be treated as a monatomic ideal gas and that the volume of solid zinc is negligible compared to the corresponding vapor. Concepts: (i) What is sublimation, and what is the latent heat of sublimation? (ii) When a solid phase changes to a gas phase, does the volume of the material increase or decrease, and by how much? (iii) As the material changes from a solid to a gas, does it do work on the environment, or does the environment do work on it? How much work is involved? (iv) In this problem we begin with heat Q and realize that it is used for two purposes: First, it makes the solid change into a gas, which entails a change DU in the internal energy of the material, DU 5 Ugas 2 Usolid. Second, it allows the expanding material to do work W on the environment. According to the conservation-of-energy principle, how is Q related to DU and W? (v) According to the fi rst law of thermodynamics, how is Q related to DU and W? Calculations: What is the change in the internal energy of zinc when 1.50 kg of zinc sublimates?

Each of two Carnot engines uses the same cold reservoir at a temperature of 275 K for its exhaust heat. Each engine receives 1450 J of input heat. The work from either of these engines is used to drive a * * pulley arrangement that uses a rope to accelerate a 125-kg crate from rest along a horizontal frictionless surface, as shown in the fi gure. With engine 1 the crate attains a speed of 2.00 m/s, while with engine 2 it attains a speed of 3.00 m/s. Concepts: (i) With which engine is the change in the crates energy greater? (ii) Which engine does more work? Explain your answer. (iii) For which engine is the temperature of the hot reservoir greater? Calculations: Find the temperature of the hot reservoir for each engine.