Suppose that there are two very large reservoirs of water, one at a temperature
ID: 1475601 • Letter: S
Question
Suppose that there are two very large reservoirs of water, one at a temperature of 95.0 °C, and one at a temperature of 21.0 °C. These reservoirs are brought into thermal contact long enough for 48350 J of heat to flow from the hot water to the cold water. Assume that the reservoirs are large enough so that the temperatures do not change significantly.
a) What is the total change in entropy resulting from this heat exchange between the hot water and the cold water?
b)Calculate the amount of energy made unavailable for work by this increase in entropy.
c) How much work could a Carnot engine do if it took in the given amount of heat (48350 J) from the hot water reservoir, and exhausted heat to the cold water reservoir?
Explanation / Answer
Th = 95 + 273 = 368 k
Tc = 21 + 273 = 294 k
Q = 48350 J
a) total change in entropy, dS = Q/Tc - Q/Th
= 48350/294 - 48350/368
= 33.1 J/k
c) efficieny of cornot engine, n = 1 - Tc/Th
= 1 - 294/368
= 0.201
we know, n = Workdone/Qin
==> Workdone = n*Qin
= 0.201*48350
= 9722.6 J
B) the amount of energy made unavailable for work, Q_out = Qin - Workdone
= 48350 - 9722.6
= 38627.4 J
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