Question

A geothermal heat pump absorbs 15 KJ/s of heat from the Earth 15 m below a house. This heat pump uses a 7.45 kJ/s compressor.

Answer 1

Answer:

COP of heat pump=3.013

COP of cycle=1.124

Explanation

W = Q2 - Q1 ----- equation 1

W = work done

Q2 = final energy

Q1 = initial energy

A) calculate the COP of the heat pump

COP =Q2/W

from equation 1

Q2 = Q1 + W = 15 + 7.45 = 22.45 KW

therefore COP =22.45/7.45  = 3.013

B) COP when cycle is reversed

COP = Q1/W

from equation 1

Q1 + W = Q2 ------ equation 2

Q2 = 15 Btu/s = 15 * 1.055 = 15.825 KW therefore from equation 2

Q1 = 8.375 KW

COP =8.375/7.45   = 1.124

Answer 2

Answer:

a) COP = 3.01

b) COP = 1.12

Explanation:

a) The heat is:

Q₂ = Q₁ + W = 15 + 7.45 = 22.45 kW

the COP of the heat pump is

COP = Q₂/W = 22.45/7.45 = 3.01

b) Operating as an air conditioner, the heat is

Q₁ = Q₂ - W = 8.375 kW

The COP is:

COP = Q₁/W = 8.375/7.45 = 1.12