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An unknown material has a normal melting/freezing point of -29.1 °C, and the liquid phase has...

An unknown material has a normal melting/freezing point of -29.1 °C, and the liquid phase has a specific heat capacity of 178 J/(kg C°). One-tenth of a kilogram of the solid at -29.1 °C is put into a 0.132-kg aluminum calorimeter cup that contains 0.165 kg of glycerin. The temperature of the cup and the glycerin is initially 26.9 °C. All the unknown material melts, and the final temperature at equilibrium is 18.0 °C. The calorimeter neither loses energy to nor gains energy from the external environment. What is the latent heat of fusion of the unknown material?

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