A town is planning on using the water flowing through a river at a rate of 5.0X10^6 kg/s to carry away the heat from a new power plant. Environmental studies indicate that the temperature of the river should only increase by 0.50ºC. The maximum design efficiency for this plant is 30.0%. What is the maximum possible power this plant can produce?

Answer 1

Equations you will need:
Q = mc deltaT
e = 1 - (Qc/Qh)

The first thing you need to realize is that when you're calculating Q it's Qc, because that is the heat going into the water and therefore out of the power station. So then you can plug that into e = 1- (Qc/Qh) and solve for Qh.

That isn't the answer yet, though, because it isn't asking how much heat the engine uses (input heat is Qh). It's asking how much total energy it can produce.

And now it's very simple because you know Qh, the total heat it uses, and you know the efficiency, the amount of that heat that can be used to do work. So you multiply Qh by the efficiency and THAT's the answer.