A Carnot refrigerator works between the temperature limits of -5°C and 23°C. Calculate the power required to run the refrigerator in case it produces 1000 kg of ice per hour at -5°C. Surrounding temperature is 23°C is 23°C. Assume reversible heat transfer, specific heat of ice as 2 kJ/kgK and that of water as 4.187 kJ/kgK and latent heat of freezing as 335 kJ/kg.

Subject:- Refrigeration and Air Conditioning

Topic:- Introduction to Refrigeration

Difficulty:- High

Let us first calculate the refrigerating capacity of the refrigerator

Heat to be removed=Sensible heat for converting water at 23°C to water at $0°C$+ latent heat for Converting water at 0°C to ice at 0°C+ Sensible heat for converting ice at 0°C to ice at -5°C

= m ̇Cp water(HT-LT)+m ̇h_fs+m ̇Cp ice(HT-LT)

=$\frac{(1000[4.187*(23-0)+335+2*(0-(-5))])}{(1 hour)}$

= 441301 kJ/hour

Therefore Capacity= 441301/3600 = 122.58 kJ/sec

T2= 296 K T1=268K

C.O.P. of refrigerating machine=$\frac{T1}{(T2-T1)}$=9.57

We know,

C.O.P.= $\frac{capacity}{(power consumed by compressor)}$

9.57= $\frac{122.58}{(power consumed by compressor)}$

∴power required to run the refrigerator

=12.81 kW