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In a cold storage, ice melts at the rate...

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`

Text Solution

Verified by Experts

The correct Answer is:
`13.67`
Mass of ice that melts per second `=(2xx1000)/3600 =5/9g`
To prevent melting of ice, heat needed to be drawn out per second, `Q_2 =mL =5/9 xx80 =400/9` cal
Also ` T_2 = 273K, T_1 = 20 + 273 = 293 K`
Coefficient of performance, `beta = Q_2/W = T_2/(T_1-T_2)`
`:. W = (Q_2(T_1-T_2))/T_2=(400 xx(293 -273))/(9 xx 273)`
`=(400xx20)/(9xx273)"cal s"^(-1)= (8000 xx 4.2)/(9 xx 273)Js^(-1)`
`:.` Minimum power output of the motor used = 13.67 W.
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