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

The temperature of well water be 288.07 K

Step-by-step explanation:

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

Work done W = 900 J

Efficiency is given by
`\eta =(W)/(Q_H)=(900)/(13900)=0.0647`

Efficiency is also given by
`\eta =1-(T_L)/(T_H)`, here
`T_L` is lower temperature and
`T_H` is higher temperature

So
`0.0647=1-(T_L)/(T_H)`

`0.0647=1-(T_L)/(308)`

`T_L=288.07K`

So the temperature of well water be 288.07 K