A carnot refrigerator absorbs heat from water at 0^(@)C and gives it to a room at 27^(@)C. Find the work done by the refrigerator and the coefficient of performance of the machine when it changes 2 kg of water at 0^(@)C to ice at 0^(@)C. Specific latent heat of ice =333 xx 10^(3) Jkg ^(-1)?

A carnot refrigerator absorbs heat from water at 0^(@)C and gives it t

1.	A carnot refrigerator absorbs heat from water at 0^(@)C and gives it to a room at 27^(@)C. Find the work done by the refrigerator and the coefficient of performance of the machine when it changes 2 kg of water at 0^(@)C to ice at 0^(@)C. Specific latent heat of ice =333 xx 10^(3) Jkg ^(-1)?
Answer» Solution :L.H. of ICE `= L = 933 xx 10 ^(3) J Kg ^(-1)` Heat absorbed from 2 kg of water at `0^(@)C= Q_(2) = mL = 2 xx 333 xx 10 ^(3) J` `= 666 xx 10 ^(3) J` `T_(2) = 0^(@)C = 273 K, T_(1) = 27 + 273 = 300 K` Heat rejected `= Q_(1) = ?` `( Q _(1))/( Q _(2)) = (T_(1))/( T _(2)) , Q_(1) = (T_(1))/(T_(2)) xx Q_(2)` ` Q _(1) = (300)/( 273) xx 666 xx 10 ^(3) = 731. 86 xx 10 ^(3) J` Word DONE ` = W = Q_(1) - Q_(2) = 731. 86 xx 10 ^(3) - 666 xx 10 ^(3) J` ` = 65.87 xx 10 ^(3) J` COEFFICIENT ofperformance `= (Q_(2))/(Q_(1) - Q_(2))` ` = ( 666 xx 10 ^(3))/( 731. 86 xx 10 ^(3) - 666 xx 10 ^(3))` `= ( 666 xx 10 ^(3))/( 65. 86 xx 10 ^(3)) = 10. 11`