Question

Solve this:
Q. A Heat Engine is used to drive a Heat-Pump (Refrigerator). The Heat transfer from the Heat Engine and from the Heat-pump are used to heat the circulating water in a plant. The Efficiency of heat engine is 30% where as WP of heat pump is 5. Calculate the heat transfer to the circulating water?

Answer 1

Let $Q_1$ be heat entering the engine and $Q_2$ and $Q_3$ be the heat transfer to water.

To find: Heat transfer to the water $\frac{Q_2+Q_3}{Q_1}$

Given:

Efficiency η = 0.3

WP of pump = 5

We know,

Work, W = η $Q_1$ = $0.3\times Q_1$

Heat transferring to the water is given as

$Q_2$ = (1-η) $Q_1$ = 0.7$Q_1$

$Q_3$ = WP x W = 5 x 0.3 x $Q_1$ = 1.5 $Q_1$

Now,

$\frac{Q_2+Q_3}{Q_1}$ =$\frac{0.7Q_1+1.5Q_1}{Q_1}=\frac{2.2Q_1}{Q_1}=2.2$

So we can say that

If the Q energy is taken by the heat engine the energy given to the water is 2.2 Q