Question

A refrigerator freezes 5kg of water at 0°C into ice at 0°C in a time interval of 20 min. Assume that room temp is 20°C. Calculate the minimum power needed to accomplish it?

Answer 1

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Answer 2

The minimum power needed to accomplish it is 102.55W.

We know that the amount of heat required to convert water at 0 °C to ice at 0 °C is by latent heat of freezing.

Heat energy released (Q) = m × L

where m is the mass of water = 5kg

L is the latent heat of freezing = 80KCal/kg

So, putting their values, we get:

Q = (5 × 80) KCal = 400 KCal

This amount of energy is released.

Room Temperature T = 20 °C = (20 + 273) K = 293 K

Converting it to 0 °C (T'). T' = 273 K

Let work done be represented as W.

We know, Q/W = (T')/(T - T')

⇒ W = Q (T - T')/T'

⇒ W = 400 (293 - 273)/273

⇒ W =  29.3 KCal = (29.3 × 10³ × 4.2) J       [1 Cal = 4.2J]

We know, Power = Work / Time

So, P = 29.3 × 10³ × 4.2 / (20 × 60)                [1 min = 60s]

⇒ P = 102.55 Watts