1. A Carnot refrigerator transfers heat from its inside (5.46 oC) to the room ai

Question

1. 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.

2. Heat Q flows spontaneously from a reservoir at 373 K into a reservoir at 298 K. Because of the spontaneous flow, 2720 J of energy is rendered unavailable for work when a Carnot engine operates between the reservoir at 298 K and a reservoir at 243 K. Find Q.

3. Find the change in entropy of the H2O molecules when (a)3.10 kilograms of ice melts into water at 273 K and (b)4.48 kilograms of water changes into steam at 373 K.

Explanation / Answer

2)

I think you need to consider the difference works done by each engine.

A heat engine operating as Carnot engine extracts the maximum available work from the heat flowing from hot reservoir into it. So the amount of work, which is rendered unavailable for work due to the temperature drop, is the same as difference in the work a Carnot engine can extract at two hot reservoir temperatures:
W = W - W

The heat engine operating between original reservoir temperatures has a thermal efficiency of:
= 1 - (Tc/Th)
So the work done by this engine is:
W = Q = (1 - (Tc/Th))Q
For the heat engine operating at lower hot reservoir temperature you get:
= 1 - (Tc/Th)
=>
W = Q = (1 - (Tc/Th))Q

So the amount of heat which is rendered to the spontaneous heat flow to hot reservoir at lower temperature is:
W = (1 - (Tc/Th))Q - (1 - (Tc/Th))Q
<=>
W = ((Tc/Th) - (Tc/Th))Q

Hence,
Q = W /((Tc/Th) - (Tc/Th))
= 2720 J / ( (243/298) - (243/373))
= 10,304.5 J

3)

a) Delta S = Q sub REV / T

For the ice melting at 273 K:

Q = ( m ) ( Lsf )

Q = ( 3.10) ( 333.7 ) = 1034.47 kJ

Delta S = Q / T

Delta S = 1034.47 / 273 = 3.789kJ / K

b) For the vaporization at 373 K :

Delta S = Q / T = ( m ) ( Lfg ) / 373

Delta S = ( 4.48 ) ( 2257 ) / 373 = 12842 / 373 = 27.108 kJ / K

The vaporization has the larger value for Delta S. Going from liquid molecules to vapor molecules

moving in all directions creates far more disorder than solid molecules melting and becoming liquid molecules

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