Refrigerator is an apparatus which takes heat from a cold body, work is done on it and the work done together with the heat absorbed is rejected to the source. An ideal refrigerator can be regarded as Carnot's ideal heat engine working in the reverse direction. The coefficient of performance of refrigerator is defined as `beta = ("Heat extracted from cold reservoir")/("work done on working substance") = (Q_(2))/(W) = (Q_(2))/(Q_(1)- Q_(2)) = (T_(2))/(T_(1) - T_(2))`

A Carnot's refrigerator takes heat from water at `0^(@)C` and discards it to a room temperature at `27^(@)C` . `1`Kg of water at `0^(@)C` is to be changed into ice at `0^(@)C. (L_(ice) = 80"kcal//kg")`
How many calories of heat are discarded to the room?

Options

A. `72.8` kcal
B. `87.9` kcal
C. `80` kcal
D. `7.9` kcal

Answer

B

Explanation

`(Q_(1))/(Q_(2)) = (T_(1))/(T_(2)) implies Q_(1) = ((T_(1))/(T_(2))) Q_(2) = ((300)/(273)) (80) = 87.9"kcal"`