Black heat capacity

Joseph Black was a pioneer in careful measurements of heat transfer, making important contributions in the areas of calorimetry, specific heat, and latent heat. The fact that different materials had different heat capacities was not widely known in his time. Here Black gives a specific example involving water and mercury (quicksilver, in his terms):
To make this plainer by an example in numbers, let us suppose the water to be at the 100th degree of heat, and that an equal measure of warm quicksilver at the 150th degree, is suddenly mixed and agitated with it. We know that the middle temperature between 100 and 150 is 125, and we know that this middle temperature would be produced by mixing the cold water at 100 with an equal measure of warm water at 150; the heat of the warm water being lowered by 25 degrees, while that of the cold is raised just as much. But when warm quicksilver is used in place of warm water, the temperature of the mixture turns out 120 degrees only instead of 125. The quicksilver, therefore, is become less warm by 30 degrees, while the water has become warmer by twenty degrees only; and yet the quantity of heat which the water has gained is the very same quantity which the quicksilver has lost.

a) By "the 100th degree of heat," Black meant 100°F. Express the original temperatures of water and mercury in °C.
b) By "equal measures", Black means equal volumes. Using modern heat capacity data, compute the final temperature that would result from mixing 100. mL water at 100.°F with 100. mL mercury at 150.°F. (The heat lost by the mercury is gained by the water.) You may find it useful to use one or more of the following pieces of information.
substancedensity (g/mL)specific heat (J/g°C)molar heat capacity (J/mol°C)
water (H2O)0.9884.1875.3
mercury (Hg)13.50.13827.7
c) Express the final temperature of the mixture in °F.

Reference

Joseph Black, Lectures on the Elements of Chemistry delivered in the University of Edinburgh by the Late Joseph Black, M.D. ... published from his manuscripts by John Robison (1803)

Copyright 2003 by Carmen Giunta. Permission is granted to reproduce for non-commercial educational purposes.

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