Page:Elementary Text-book of Physics (Anthony, 1897).djvu/208

194 degree as is required to raise the temperature of a kilogram of water through the same range. In order to raise the temperatures of other substances through the same range, quantities of heat peculiar to each substance are required.

The quantity of heat required to raise the temperature of one kilogram of a substance from zero to one degree is called the specific heat of the substance.

If the temperature of one kilogram of a substance rise from $$t_{0}$$ to $$t,$$ the limit of the ratio of the quantity of heat required to bring about the rise in temperature to the difference in temperature, as that diSerence diminishes indefinitely, is called the specific heat of the substance at temperature $$t.$$ If we represent the quantity of heat by $$Q,$$ the limit of the ratio $$\frac{Q}{t - t_{0}} = \frac{dQ}{dt}$$ expresses this specific heat.

The specific heats of substances are generally nearly constant between zero and one hundred degrees. The mean specific heat of a substance between zero and one hundred degrees is the one usually given in the tables.

The measurement of specific heat is one of the important objects of calorimetry.

167. Ice Calorimeter.—Black's or Wilcke's ice calorimeter consists of a block of pure ice having a cavity in its interior covered by a thick slab of ice. The body of which the specific heat is to be determined is heated to t degrees, then dropped into the cavity, and immediately covered by the slab. After a short time the temperature of the body falls to zero, and in so doing converts a certain quantity of ice into water. This water is removed by a sponge of known weight, and its weight is determined. It will be shown, that to melt a kilogram of ice requires 80 calories; if, then, the weight of the body be $$P,$$ and its specific heat $$c,$$ it gives up, in falling from $$t$$ degrees to zero, $$Pct$$ calories. On the other hand, if $$p$$ kilograms of ice be melted, the heat required is $$80p.$$ Therefore $$Pct = 80p;$$ whence