Page:Elementary Text-book of Physics (Anthony, 1897).djvu/212

198 Eliminating $$M,$$ we obtain '''171. Determination of the Mechanical Equivalent of Heat.'''— It has been stated that whenever heat is produced by the expenditure of mechanical energy, the quantity of heat produced is always proportional to the quantity of mechanical energy expended.

The mechanical equivalent of heat is the energy in mechanical units, the expenditure of which produces the unit of heat.

Heat applied to a body may increase the motion of its molecules; that is, add to their kinetic energy. It may perform internal work by moving the molecules against molecular forces. It may perform external work by producing motion against external forces. If we could estimate these effects in mechanical units, we might obtain the mechanical equivalent of heat. But the kinetic energy of the molecules cannot be estimated, for we do not know their mass or their velocity. We must, therefore, in the present state of our knowledge, resort to direct experiment to determine the heat equivalent. In one of the experiments of Joule, already referred to, a paddle-wheel was made to revolve, by means of weights, in a vessel filled with water. In this vessel were stationary wings, to prevent the water from acquiring a rotary motion with the paddle-wheel. By the revolution of the wheel the water was warmed. The heat so generated was estimated from the rise of temperature, while the mechanical energy required to produce it was given by the fall of the driving weight. Joule repeated this experiment, substituting mercury for the water. In another experiment he substituted an iron plate for the paddle-wheel, and made it revolve with friction upon a fixed iron plate under water.

Joule expressed his results in kilogram-metres—that is, the work done by a kilogram in falling under the force of gravity through one metre. He stated the mechanical equivalent of one calorie, in this unit, to be 423.9, from the experiments with water; 425.7, from those with mercury; and 426.1, from those with iron