In a cold storage, ice melts at the rate of `2 kg//h` when the external temperature is `20^(@)C`. Find the minimum power output of the motor used to drive the refrigerator which just prevents the ice from melting. Latent heat of fusion of `ice = 80 cal//g`

Answer

`13.67W`

Explanation

Mass of ice melted/sec. `=(2xx1000)/(60xx60)=5/9gram`
To prevent melting, heat to be drawn out/sec.
`Q_(2)=5/9xx80 cals. = (400)/9 cals.`
`T_(2)= 273K, T_(1)= 20^(@)C= 20+273=293K`.
`C.O.P= (Q_(2))/W= (T_(2))/(T_(2))`
`W=(Q_(2)(T_(1)-T_(2)))/(T_(2))=(400(293xx273))/(9xx273)`
`=(400xx20)/(9xx273)cal//s=(8000xx4.2)/(9xx273) "joule"//s`
i.e., Power of motor `= 13.67 "watt"`