Page:Elementary Text-book of Physics (Anthony, 1897).djvu/229

§ 199] begins the rise of temperature ceases. Whatever the heat to which a solid may be exposed, it cannot be made hotter than its melting-point. When ice is melted by pressure its temperature is lowered. When a liquid is cooled, its fall of temperature ceases when solidification begins; and if, as may occur under favorable conditions, a liquid is cooled below its melting-point, its temperature rises at once to the melting-point, when solidification begins. Heat, therefore, disappears when a body melts, and is generated when a liquid becomes solid.

It was stated (§ 159) that ice can be melted by friction; that is, by the expenditure of mechanical energy. Fusion is, therefore, work which requires the expenditure of some form of energy to accomplish it. The heat required to melt unit mass of a substance is the heat equivalent of fusion of that substance. When a substance solidifies, it develops the same amount of heat as was required to melt it.

As will be shown later at greater length, the absorption of heat which occurs when a solid is melted is explained by supposing that it is used in doing work against the forces which determine the direction of the molecules in the solid and in increasing the kinetic energy of molecular translation.

199. Determination of the Heat Equivalent of Fusion.—The heat equivalent of fusion may be determined by the method of mixtures (§ 168), as follows: A mass of ice, for example, represented by $$P,$$ at a temperature $$t$$ below its melting-point, to insure dryness, is plunged into a mass $$P'$$ of warm water at the temperature $$T.$$ Represent by $$\theta$$ the resulting temperature, when the ice is all melted. If $$p$$ represent the water equivalent of the calorimeter, $$(P' + p) (T - \theta)$$ is the heat given up by the calorimeter and its contents. Let $$c$$ represent the specific heat of ice, and $$x$$ the heat equivalent of fusion. The ice absorbs, to raise its temperature to zero, $$Ptc$$ calories; to melt it, $$Px$$ calories; to warm the water after melting, $$P\theta$$ calories. We then have the equation from which $$x$$ may be found.