Determine the power:

The capacity of any refrigerator is 200 TR while working among - 6°C & 25^oC. Find the mass of ice formed per day from water at 25°C. Also determine the power needed to drive the unit. Consider that the cycle operates on reversed Carnot cycle & latent heat of ice is 335 kJ/kg.

Solution

It is given: Q = 200TR; T₁ = - 6°C = -6 + 273 = 267 K; T₂ = 25°C;

T_w = 250 C : hfg = 335 kJ/kg

Mass of ice formed per day

As we know that heat extraction capacity of the refrigerator

= 200 * 210 = 42000 kJ/min

heat eliminated from 1 kg of water at 25°C to produce ice at 0°C (1 TR = 210 kJ/min)

= Mass * Sp. heat *Rise in temperature + hfg (ice)

= 1 * 4.187 (25 - 0) + 335 = 439.7 kJ/kg

Mass of ice formed per min

= 42000/439.7

 = 95.52 kg/min

and mass of ice formed per day = 95.52 *60 *24 = 137550 kg = 137.55 tonnes Power needed to drive the unit

As we know that C.O.P. of the reversed Carnot cycle

COP. = (Heat extraction capacity)/(Work done per mm)

 Work performed per min = 42 000/8.6 = 4884 kJ/min

Power needed to drive the unit

4884/60

= 81.4 kW        Ans.