Question

The water in a deep underground well is used as the cold resevoir of a Carnot heat pump that maintains the temperature of a house at 308 K. To deposit 13900 J of heat in the house, the heat pump requires 900 J of work. Determine the temperature of the well water.

Answer 1

Answer:

The temperature of well water be 288.07 K

Explanation:

We have given Heat in house $Q_H=13900J$

Work done W = 900 J

Efficiency is given by $\eta =\frac{W}{Q_H}=\frac{900}{13900}=0.0647$

Efficiency is also given by $\eta =1-\frac{T_L}{T_H}$, here $T_L$ is lower temperature and $T_H$ is higher temperature

So $0.0647=1-\frac{T_L}{T_H}$

$0.0647=1-\frac{T_L}{308}$

$T_L=288.07K$

So the temperature of well water be 288.07 K