Question

calculate the required electric energy in k joules for an electric refrigator with motor working between 30c and 5c to freez 3kg of water at 0c the latent heat of water-ice is 80 cal/gm

Answer 1

Answer on Question #43176-Physics-Molecular Physics-Thermodynamics

Calculate the required electric energy in k joules for an electric refrigerator with motor working between 30c and 5c to freeze 3kg of water at 0c the latent heat of water-ice is 80 cal/gm.

Solution

The refrigeration efficiency is

$$\eta = \frac {Q}{W} = \frac {T _ {2}}{T _ {1} - T _ {2}}.$$

Hence

$$W = Q \frac {T _ {1} - T _ {2}}{T _ {2}}.$$

$Q = ML$ is latent heat for $M = 3\mathrm{kg}$ of water at $T = 0{}^{\circ}\mathrm{C}$ to become ice. As

$$L = 8 0 \frac {\mathrm {cal}}{\mathrm {gm}} = 3.35 \cdot 10^{5} \frac {J}{kg}.$$

we find

$$W = 3.35 \cdot 10^{5} \frac {J}{kg} \cdot 3 \mathrm{kg} \frac {25K}{278.15K} = 90.3 \cdot 10^{3} J = 90.3 kJ$$

Answer: 90.3 kJ.

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