Common opinion had held that to melt a solid required only a tiny addition of heat once the solid had been raised to its melting temperature. Black noted that the quantity of heat required was actually substantial. He gave the term latent heat to the "hidden" heat required to bring about a phase transition in addition to heating a material to the proper temperature.
I have ... put a lump of ice into an equal quantity of water, heated to the temperature 176[°F], and the result was, that the fluid was no hotter than water just ready to freeze. Nay, if a little sea salt be added to the water, and it be heated only to 166 or 170, we shall produce a fluid sensibly colder than the ice was in the beginning, which has appeared a curious and puzzling thing to those unacquainted with the general fact.1) Using modern data on the heat capacity of water, find the latent heat of fusion of one mole of water. Assume that Black placed 100. g of ice at 0.0°C in a well-insulated container with 100. g of water at 80.0°C (176°F). Of course, the hot water melts the ice and the cold ice cools the water. Assume that the result of this heat exchange is 200. g of liquid water at 0.0°C. The molar heat capacity of liquid water is 75.3 J/mol°C .
2) Qualitatively rationalize how Black's salt-water variation is possible: how can one mix equal masses of ice at 0°C and salt water at, say, 75°C, and end up with salt water at a temperature below zero?
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