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Question:

A Carnot freezer takes heat from water at 0°C inside it and rejects it to the room at a temperature of 27°C. The latent heat of ice is 336 × 10³ J/kg. If 5 kg of water at 0°C is converted into ice at 0°C by the freezer, then the energy consumed by the freezer is close to:

1.68 × 10⁶ J

1.71 × 10⁷ J

1.67 × 10⁵ J

1.51 × 10⁵ J

Solution:

Δθ = mL = 5 × 336 × 10³ = Qsink
Qsink/Qsource = Tsink/Tsource
∴ Qsource = Tsource/Tsink × Qsink
∴ E = Qsource - Qsink = Qsink(Tsource/Tsink - 1) = 5 × 336 × 10³(300/273 - 1) = 1.67 × 10⁵ J