1.A Carnot engine operates between temperatures of 760 and 341 K. Calculate what

Question

1.A Carnot engine operates between temperatures of 760 and 341 K. Calculate what the efficiency would be if (a) the temperature of the hot reservoir were raised by 53.4 K or (b) if the temperature of the cold reservoir were lowered by 53.4 K. (Give a decimal number between zero and one in both cases.)

2.A Carnot refrigerator transfers heat from its inside (5.46 oC) to the room air outside (23.2 oC). (a) Find the coefficient of performance of the refrigerator. (b) Determine the magnitude of the minimum work needed to cool 4.32 kg of water from 23.2 to 5.46 oC when it is placed in the refrigerator.

3.Heat Q flows spontaneously from a reservoir at 368 K into a reservoir at 298 K. Because of the spontaneous flow, 2870 J of energy is rendered unavailable for work when a Carnot engine operates between the reservoir at 298 K and a reservoir at 235 K. Find Q.

Explanation / Answer

1)   a)    Carnot efficiency = (Th - Tc)/Th

                                        =    (472.4/813.4)

                                         = 0.58077

    b)     Carnot efficiency =   (472.4/760)

                                         = 0.62157

2)    a)   coefficient of performance of the refrigerator =    Th/(Th - Tc)

                                                                               = 296.35/17.74

                                                                               =   16.705

b)    Here, Q/W = COP

=> (4.32 * 4186 * 17.74)/W = 16.705

=> W =   19203.92 J

c)       Here,     Q =   (0.21/0.19) * 2870

                          = 3193.39 J

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