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Exam 21: Heat Engines and Refrigerators

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Question 1

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During each cycle of operation, a refrigerator absorbs 230 J of heat from the freezer and expels 356 J of heat to the room. How much work input is required in each cycle?

A) 712 J
B) 586 J
C) 460 J
D) 310 J
E) 126 J

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Question 2

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A refrigerator has a coefficient of performance of 1.15, and it extracts 7.95 J of heat from the cold reservoir during each cycle. (a) How much work is done on the gas in each cycle? (b) How much heat is exhausted into the hot reservoir in each cycle?

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(a) 6.91 J (b) 14.9 J

Question 3

Multiple Choice

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A refrigerator removes heat from the freezing compartment at the rate of 20 kJ and ejects 24 kJ into a room per cycle. How much work is required in each cycle?

A Carnot air conditioner operates between an indoor temperature of 20°C and an outdoor temperature of 39°C. How much energy does it need to remove 2000 J of heat from the interior of the house?

What is the change in entropy of 10.0 moles of ideal monatomic gas that reversibly undergoes the isothermal expansion shown in the figure? The ideal gas constant is R = 8.314 J/(mol ∙ K) .

A refrigerator has a coefficient of performance equal to 4.2. How much work must be done on the refrigerator in order to remove 250 J of heat from the interior?

A Carnot engine is operated as a heat pump to heat a room in the winter. The heat pump delivers heat to the room at the rate of per second and maintains the room at a temperature of when the outside temperature is The power requirement for the heat pump under these operating conditions is closest to

Is it possible to transfer heat from a hot reservoir to a cold reservoir?

An air conditioner with a coefficient of performance of 3.5 uses 30 kW of power. How much power is it discharging to the outdoors?

A Carnot refrigerator has a coefficient of performance of 2.5. The refrigerator consumes 50 W of power. How much heat is removed from the interior of the refrigerator in 1 hour?

A Carnot cycle engine operates between a low temperature reservoir at 20°C and a high temperature reservoir at 800°C. If the engine is required to output 20.0 kJ of work per cycle, how much heat must the high temperature reservoir transfer to the engine during each cycle?

A brass rod, 75.0 cm long and having a cross-sectional area of 2.50 cm², conducts heat from a large furnace at 375°C into a very large cold water bath at 10.0°C without losing any heat at the lateral surface of the rod. Steady state has been established, and the thermal conductivity of brass is . The rate at which the entropy of the system (furnace plus water) is changing is closest to

A heat engine with an efficiency of 30.0% performs 2500 J of work. How much heat is discharged to the lower temperature reservoir?

What is the maximum theoretical efficiency possible for a heat engine operating between a reservoir in which ice and water coexist, and a reservoir in which water and steam coexist? The pressure is constant at 1.0 atmosphere for both reservoirs.

A Carnot engine operates between a high temperature reservoir at and a river with water at If it absorbs of heat each cycle, how much work per cycle does it perform?

One of the most efficient engines built so far has the following characteristics: combustion chamber temperature = 1900°C exhaust temperature = 430°C 7.0 × 10⁹ cal of fuel produces 1.4 × 10¹⁰ J of work in one hour, where 1 cal = 4.19 J (a) What is the actual efficiency of this engine? (b) What is the Carnot efficiency of the engine? (c) What is the power output of this engine?

A real (non-Carnot) heat engine, operating between heat reservoirs at temperatures of and performs 4.3 kJ of net work and rejects of heat in a single cycle. The thermal efficiency of this heat engine is closest to

A Carnot engine operating between a reservoir of liquid mercury at its melting point (233 K) and a colder reservoir extracts of heat from the mercury and does of work during each cycle. What is the temperature of the colder reservoir?

An ideal Carnot engine operates between reservoirs having temperatures of 125°C and -20°C. Each cycle the heat expelled by this engine is used to melt 30.0 g of ice at 0.00°C. The heat of fusion of water is 3.34 × 10⁵ J/kg and the heat of vaporization of water is 2.25 × 10⁶ J/kg. (a) How much work does this engine do each cycle? (b) How much heat per cycle does this engine absorb at the hot reservoir?

A certain engine extracts 1300 J of heat from a hot temperature reservoir and discharges 700 J of heat to a cold temperature reservoir. What is the efficiency of this engine?