Question

A large heat pump should upgrade 5 MW of heat at 85°C to be delivered as heat at 150°C. Suppose the actual heat pump has a COP of 2.5. How much power is required to drive the unit? For the same COP, how high a high temperature would a Carnot heat pump have, assuming the same low T?

Answer 1

W=2 MW

Step-by-step explanation:

Given that

COP= 2.5

Heat extracted from 85°C

Qa= 5 MW

Lets heat supplied at 150°C = Qr

The power input to heat pump = W

From first law of thermodynamics

Qr= Qa+ W

We know that COP of heat pump given as

`COP=(Qr)/(W)`

`2.5=(5)/(W)`

`2.5=(5)/(W)`

W=2 MW

For Carnot heat pump

`COP=(T_2)/(T_2-T_1)`

`2.5=(T_2)/(T_2-(273+85))`

2.5 T₂ - 895= T₂

T₂=596.66 K

T₂=323.6 °C