We have a heat engine taking in heat at a rate of 100 MW from a high temperature reservoir. 75 MW of

We have a heat engine taking in heat at a rate of 100 MW from a high temperature reservoir. 75 MW of this energy is rejected to a low temperature reservoir. The rest is converted to useful work. How much net work output does this heat engine produce and how efficient is it?

The only source of energy in the system is Q_H, so we know that the energy leaving in the form of W_net out and Q_L must be equal to the energy input, Q_H. Or, put another way, W_net out must be equal to the difference between Q_H and Q_L.

In this case, we get a net work output of 25 MW from this engine.

Efficiency is the ratio of your desired output to your input. In this case, the output we care about is useful work, and the input to the system is Q_H. So we get a thermal efficiency for the engine of 25%.