Chapter 16, Problem 21P

Set Up: For an engine, W and Q_H positive and Q_C is negative. For a refrigerator, Q_C is positive and W and Q_H are negative. A heat pump air conditioner takes in heat at a cool place and expels heat into a warm place. A heat pump house heater takes in heat at a cool place and expels heat into a warm place. For both types of heat pumps, W is negative and energy must be supplied to operate the device, bc and da are adiabatic, so the heat flow for these processes is zero.

Solve: (a) The cycle is clockwise. More positive work is done during ab and bc than the magnitude of the negative work done in cd and da, so the net work done in the cycle is positive. Heat enters the gas in ab and leaves the gas in cd.

(b) The cycle is counterclockwise and the net work done in the cycle is negative. Heat enters the gas in dc and leaves the gas in ba. dc occurs inside the food compartment and ba occurs in the air of the room.

(c) The cycle is counterclockwise and the net work done w the cycle is negative. Heat enters the gas in dc and leaves the gas in ba. dc occurs inside the house and ba occurs outside.

(d) The cycle is counterclockwise and the net work done in the cycle is negative. Heat enters the gas in dc and leaves the gas in ba. dc occurs outside and ba occurs inside the house.

Reflect: For a refrigerator the signs of W, Q_H, and Q_C are all opposite to what they are for an engine.

21. The pV diagram in Figure 16.17 shows a general Carnot cycle for an engine, with the hot and cold thermal reservoir segments identified. Segments ab and cd are isothermal, while the other two are adiabatic. (a) If this engine is used as a heat engine, what is the direction of the cycle, clockwise or counterclockwise? In which segments does heat enter the gas, and in which ones does it leave the gas? (b) If the engine is used as a refrigerator, what is the direction of the cycle? In which segments does heat enter the gas, and in which ones does it leave the gas? Also, which segments take place as the inside of the refrigerator, and which ones occur in the air of the room in which the refrigerator is operating? (c) If the engine is used as a heat pump–air conditioner, what is the direction of the cycle, and in which segments does heat enter the gas and in which ones does it leave the gas? Which segments take place inside of the house and which ones occur outside? (d) If the engine is used as a heat pump-house heater, what is the direction of the cycle? In which segments does heat enter the gas and in which ones does it leave the gas? Which segments take place inside of the house and which ones occur outside?

Figure 16.17

Problem 21.