Suppose that there are two very large reservoirs of water, one at a temperature
ID: 3893112 • Letter: S
Question
Suppose that there are two very large reservoirs of water, one at a temperature of 85 C, and one at a temperature of 17 C. These reservoirs are brought into thermal contact long enough for 32650 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? Answer in J/K
b) Calculate teh amount of work made unavailable by this increase in entropy. Answer in J
c) How much work could a Carnot engine do if it took in the given amount of heat (32650 J) from the hot water reservoir, and exhausted heat to the cold water reservoir? Answer in J
a) What is the total change in entropy resulting from this heat exchange between the hot water and the cold water? Answer in J/K
b) Calculate teh amount of work made unavailable by this increase in entropy. Answer in J
c) How much work could a Carnot engine do if it took in the given amount of heat (32650 J) from the hot water reservoir, and exhausted heat to the cold water reservoir? Answer in J
Explanation / Answer
A) change in entropy =change in Q/T
for reservoir at T =85C =358 K heat is lost so change in Q= -32650
give change in S= -32650/358=-91.20 J/K
for second reservior T= 290 k heat taken so Q +ve
so change of S = 32650/290=112.58 J/K
so net total change in entropy = 112.58 - 91.20=21.38 J/K
unavailable work = T( change in S) = 358*(21.38)=7643.3 J
for carnot engine W/Q =1-(T1/T2) so W= 32650(1-290/358)=6201.67 J
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