Air Refrigeration Cycles (Mathematical Problem-1)

## An ice plant produces 10 tonnes of ice per day at 0^oC using water at room temperature of 20^oC. Estimate the power rating of the compressor motor, if the C.O.P of the plant is 2.5 and overall electro-mechanical efficiency is 90%.

Solution:

Given,

            m= 10 ton/day = 10 x 1000/24 x 60= 6.94 Kg/min,

            T₁= 0^oC=273 K

            T₂ = 20^oC =293 K

            C.O.P = 2.5

            Efficiency ɳ_o=90%=0.9

Let, W=Work required to drive the compressor /min
We know that, Heat extracted from 1 Kg of water at 20^oC to produce 1 Kg of ice at 0^oC
               = 1 x 4.187 (20-0) + 335             :: Latent heat of ice= 335 KJ/Kg
               = 418.74 KJ/Kg

So, Total heat extracted,  Q= 418.74  x 6.94 = 2906 KJ/min

We also know that, C.O.P of the plant,

                  2.5 = Q/W

                        = 2906/W

                   W = 2906/2.5 

                   W = 1162.4 KJ/min.

and Power required,

                    P = 1162.4/ (60 x ɳ_o) 

                       = 1162.4/ (60 x 0.9)  

                       = 21.5 KW

So, the power rating of the compressor motor = 21.5 KW