A carnot engine having a perfect gas aas the working substance is driven backwards and is used for freezing water already at `0^(@)C`. If the engine is driven by `500W` electric motor with an efficiency of `60%` how long will it take to freeze `15kg` of water? The working temps of the engine are `15^(@)C` and `0^(@)C`. The system involves no energy losses. Given latent heat of ice `=333xx10^(3)J kg^(-1)`.

Explanation

Here, `T_(1)= 0^(@)C=(0+273)K`
`=273K, m= 15kg`
`T_(2)= 15^(@)C= (15+273)= 288K, p= 500 "watt" `,
`eta= 60%, L=333xx10^(3)Jkg^(-1)`.
Useful power of motor `=60%(500)"watt"`
`=300W=300Js^(-1)`
i.e., `W=300Js^(-1)`
Coeff. Of performance of refrigerator
`beta=(Q_(2))/W= (T_(2))/(T_(1)-T_(2))`
`:. Q_(2)=(T_(2)W)/(T_(1)-T_(2))=(273xx300)/(288-273)= 5460Js_(1)`
Total heat to be drwan from `15 Kg` water to freeze it `Q-mL=15xx333xx10^(3)J`
`:. Time taken= Q/(Q_(2))= (15xx333xx10^(3))/(5460)`
`=914.8 s`