Question

Suppose that there are two very large reservoirs of water, one at a temperature of 87.0...

Suppose that there are two very large reservoirs of water, one at a temperature of 87.0 ∘C and one at a temperature of 19.0 ∘C. These reservoirs are brought into thermal contact long enough for 40210 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, Δ?tot, resulting from this heat exchange between the hot water and the cold water?

Calculate the amount of energy made unavailable for work by this increase in entropy.

How much work could a Carnot engine do if it took in the given amount of heat (40210 J) from the hot water reservoir and exhausted heat to the cold water reservoir?

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Answer #1

Given.

The temperature of Hot reservoir Th = 87∘C = 360 K

The temperature of Cold reservoir Tc = 19∘C = 292 K

Heat flow from the hot water to the cold water. Q = 40210 J

Therefore for the Carnot engine, the change in entropy can be calculated as

Now to determine the work a Carnot engine could do if it took in the given amount of heat (40210 J) from the hot water reservoir and exhausted heat to the cold water reservoir.

We have to first determine the efficiency of the engine. Ef

Now work done can be calculated as follows.

Hence The work done is 7574.656 J

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