AZING!The Second Law of Thermodynamics and Entropy Changes in a Heat Engine

[Peter G.]

Hi,

A heat engine operates between a high-temperature source and a sink at a lower temperature as shown below:

The diagram shows a hot reservoir transferring energy to a engine that does work and dissipates the remaining energy into a cold sink.

The question is: There is a gain in entropy as a result of the engine doing work W. Identify two further entropy changes and, by reference to the second law of thermodynamics, state how the three changes are related.

My attempt:

Entropy is lost by the hot reservoir as energy is transferred to the engine (entropy gained by engine). The relation is this enables the engine to perform work, leading to a decrease in entropy of the engine and an increase in entropy of the surroundings. Finally, the last one I identified regarded the loss of entropy by the engine and gain by the cold sink as the engine transfers thermal energy to the cold sink for the engine can't be 100% efficient.

Marking scheme

Gain G when thermal energy transferred to sink/cold reservoir; loss L when thermal energy transferred from source/hot reservoir; the overall / total entropy of the universe increases; law implies

What I said fits? Did I go wrong somewhere?

Thanks in advance,
Peter G.

 

[Andrew Mason]

The question is: There is a gain in entropy as a result of the engine doing work W. Identify two further entropy changes and, by reference to the second law of thermodynamics, state how the three changes are related.

My attempt:

Entropy is lost by the hot reservoir as energy is transferred to the engine (entropy gained by engine). The relation is this enables the engine to perform work, leading to a decrease in entropy of the engine and an increase in entropy of the surroundings. Finally, the last one I identified regarded the loss of entropy by the engine and gain by the cold sink as the engine transfers thermal energy to the cold sink for the engine can't be 100% efficient.

Marking scheme

Gain G when thermal energy transferred to sink/cold reservoir; loss L when thermal energy transferred from source/hot reservoir; the overall / total entropy of the universe increases; law implies

What I said fits? Did I go wrong somewhere?

The gain in entropy referred to in the question is the overall change in entropy of the system + surroundings. There are two entropy changes that contribute to this: the decrease in entropy of the hot reservoir and the (larger in magnitude) increase in entropy of the cold reservoir. That is all. The engine operates on a cycle so it returns to its original state at the completion of each cycle. This means that the engine itself experiences no change in entropy.

AM