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A carnot engine having a perfect gas aas...

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)`.

Text Solution

Verified by Experts

Given `T_(1)=273K`
`T_(2)=15+273=280K`
Useful power `=etaP`
`=0.6xx500=300J//s`
We know that coefficient of performance
`beta=(Q_(2))/W=((T_(2))/(T_(1)-T_(2)))`
`=300xx(273/(288-273))=5460J//s`
Heat needed tomelt the ice
`Q=mL=15xx333xx10^(3)J`
Time taken in freezing water
`t=Q/(Q_(2))=(15xx333xx10^(3))/5640=914.8s`
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