# Latent Heat

(Please see attachment)

A cylinder is fitted with a piston and is in thermal contact with a heat bath at 273 K. Initially the volume in the cylinder is filled with 10 kg of pure water and about half of this is liquid and other half is solid. The piston is lowered so as to reduce the volume by 2 x 10^-5 m^3. What is the magnitude and sign of heat transferred to the bath.

Density of liquid water 10^3 kg/m^3, density of ice 0.92 x 10^3 kg/m^3, latent heat of fusion of ice 333 kJ/kg.

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#### Solution Preview

Please refer attachment.

Initial volume of ice = Vi = Mass of ice/Density of ice = 5/0.92x103 = 5.435 x 10-3 m3

Initial volume of water = Vw = Mass of water/Density of water = 5/103 = 5 x 10-3 m3

Total initial volume of ice & water in cylinder = 5.435 x 10-3 + 5 x 10-3 = 10.435 x 10-3 m3

Reduction in volume ...

#### Solution Summary

The expert examines liquid water and the latent heat of fusion of ice. The magnitude and sign of heat transferred to the bath is determined.