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 93.0 °C, and one at a temperature of 17.0 °C. These reservoirs are brought into thermal contact long enough for 49710 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 (49710 J) from the hot water reservoir, and exhausted heat to the cold water reservoir?

Suppose that there are two very large reservoirs of water, one at a temperature of 93.0 , and one at a temperature of 17.0 °C. These reservoirs are brought into thermal contact long enough for 49710 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 toahange in entropy resulting from this heat exchange belweenthetr nd the cold water? Number J/K Calculate the amount of energy made unavailable for work by this increase in entropy. Number How much work could a Camot engine do if it took in the given amount of heat (49710 J) from the hot water reservoir, and exhausted heat to the cold water reservoir? Number Previous Give Up & View Solution O Check Ansi Hint How is entropy defined in terms of a heat exchange Q at some temperature T? How is an increase in entropy related to a decrease in the amount of energy available for work?

Explanation / Answer

a) dStotal = dShot + dScold

dScold = Q/Tcold ---> Tcold = 17+273 = 290 K
dShot = -Q/Thot ---> Thot = 93+273 = 366 K

dStotal = Q(1/Tcold - 1/Thot)

dS = 49710(1/290 - 1/366)
dS = 35.59 J/K

c) the work for a carnot engine is calculated like this:

W = Q*Eff ---> Eff = 1 - Tc/Th
W = 49710 * (1-290/366)
W = 10322.3 J

b) W = dS * Ti
W = 35.59 * 290 = 10321.1 J

Hope this helps

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