Question

Consider a heat engine that is 40% efficient and operating with a furnace at a temperature of 727oC with a cooling reservoir at 27oC

•A. If the heat engine withdraws 1MJ/s from the furnace, what is the rate of entropy loss from the furnace?

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•B. What would be the rate of entropy gain in the cold reservoir?

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•C. What is the total entropy gain of the system?

D. Do A , B, and C again with zero efficiency ?

Please explain your steps

Answer 1

A) First, you must remember the expression for eficiency in a heat engine:

Where Q_h is the heat energy taken from the furnace (Q_h always is a negative value), Qc is the heat energy delivered to the reservoir. Both values can be calculated with the following equations:

You know the energy withdraw from the furnace, that is Qh= 1 MJ/s and the temperature of the furnace (T_h=727 °C=1000 K), so you can calculate the rate of entropy loss from the furnace :

B)Now taking into account the efficiency expression, you can calculate Q_c as follows:

Now, you can determine the rate of entropy gain in the cold reservoir as follows:

Tc=27 °C=300 K

C)Therefore, the total entropy gain of the system would be:

D)When  eficiency is zero, you can say that:

Therefore:

Then, if the Furnace and Reservoir temperatures are the same, the entropy changes will be:

And:

Finally, the the total entropy gain of the zero efficiency system would be:


Therefore, we can say that the less efficiency is, the higher entropy gain will be.