Suppose that there are two very large reservoirs of water, one at a temperature

Question

Suppose that there are two very large reservoirs of water, one at a temperature of 95.0 degree C, and one at a temperature of 11. 0 degree C. These reservoirs are brought into thermal contact long enough for 36770 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. What is the total change in entropy resulting from this heat exchange between the hot water and the cold water? Calculate the amount of energy made unavailable this increase in entropy. How much work could a Carnot engine do if it took in the given amount of heat (36770 J) from the hot water reservoir, and exhausted heat to the cold water reservoir?

Explanation / Answer

(a)

Total entropy change of the system,

del S_total = -Q/TH+ Q/TL = -36770/(95+273) + 36770/11+273= 29.55J/K

(b)

unavailiable work

W = T_min del S = (11+273) ( 29.55) = 8393 J

(c)

e= 1- Tmin/ Tmax = 1- 284/368 = 0.228

W = Q e = 36770(0.228) = 8393 J

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