Question

A heat engine absorbs 2500 J of heat from a hot reservoir and expels 1000 J to a cold reservoir. When it is run in reverse, with the same reservoirs, the engine pumps 2500 J of heat to the hot reservoir, requiring 1500 J of work to do so. Find the ratio of the work done by the heat engine to the work done by the pump. Is the heat engine reversible?

Answer 1

To solve this problem, we must simply use the concept of Total Energy transferred both in terms of work and heat. This is basically conjugated in the first law of thermodynamics.

If we take the heat absorbed as positive and the expelled as negative we have that the total work done in the heat engine is

$W_1 = 2500-1000$

$W_1 = 1500J$

For the case of the engine pumps the Energy absorbed is

$W_2 = 1500J$

In this way the ratio between the two would be

$Ratio = \frac{W_1}{W_2} = \frac{1500}{1500} = 1$

So it is reversible, because the state of efficiency of the body is totally efficient.