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 309 K. To deposit 14100 J of heat in the house, the heat pump requires 737 J of work. Determine the temperature of the well water.

Answer 1

In Carnot heat pump it's given that

Qh = heat given (hot reservoir) = 14100 J

W = Work done required = 737 J

We know that

Qc = Heat extracted (Cold reservoir) = Qh - W

Qc = 14100 - 737 = 13363 J

Also given that

Th = temperature of hot reservoir = 309 K

Tc = temperature of cold reservoir = ? K

efficiency in carnot cycle is given by:

n = 1 - Qc/Qh = 1 - Tc/Th

Qc/Qh = Tc/Th

Tc = Th*(Qc/Qh)

Using known values:

Tc = 309*(13363/14100)

Tc = 292.85 K = 293 K = Temperature of well water

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