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`

Options

A. `28.5 W`
B. `9.75 W`
C. `16.4 W`
D. `13.6 W`

Answer

D

Explanation

`omega = (T_(2))/(T_(1)-T_(2)) = (273)/(293-273) = (273)/(20)` ltbr gt Mass of ice melting per second `= (2xx1000)/(3600) = (5/9)g`
To prevent the melting of ice, heat to be driven out per
second i.e., `Q_(2) = (5/9)xx80=400/9 cal = 186J`
As, `omega = (Q_2)/(W) , W=(Q_2)/(omega) = (186)/((273//20)) = 13.6J`
Power of the motor = `13.6W`.