Question

What is the maximal coefficient of performance of a refrigerator which cools down 10 kg of water (and then ice) to -6C. Upper heat source of this refrigerator is surroundings at constant temperature 21C. Initially water is in equilibrium with surroundings. What is maximal coefficient of performance of heat pump operating in the same configuration. Specific heat of water, specific heat of ice, and latent heat of fusion are equal to 4.19KJ/kg/K, 2.1KJ/kg/K and 335 KJ/kg, respectively.

Answer 1

Given:

Temperature of water, $T_{1}$ = $-6^{\circ}C$ =273 +(-6) =267 K

Temperature surrounding refrigerator, $T_{2}$ = $21^{\circ}C$ =273 + 21 =294 K

Specific heat given for water, $C_{w}$ = 4.19 KJ/kg/K

Specific heat given for ice, $C_{ice}$ = 2.1 KJ/kg/K

Latent heat of fusion,  $L_{fusion}$ = 335KJ/kg

Solution:

Coefficient of Performance (COP) for refrigerator is given by:

Max $COP_{refrigerator}$ = $\frac{T_{2}}{T_{2} - T_{1}}$

= $\frac{267}{294 - 267}$ = 9.89

Coefficient of Performance (COP) for heat pump is given by:

Max $COP_{heat pump}$ = $\frac{T_{1}}{T_{2} - T_{1}}$$\frac{294}{294 - 267}$ = 10.89