Page:Elementary Text-book of Physics (Anthony, 1897).djvu/253

§ 224] This is a cubic equation, and, for given values of $$p$$ and $$T,$$ will have three roots, which are either all real or of which one is real and the others imaginary, depending upon the values of the constants and on the particular values chosen for $$p$$ and $$T.$$ The existence of three real roots shows that for the assumed values of pressure and temperature three different volumes are possible; one of these is the volume of the body as a gas, another its volume as a liquid, and the third its volume in an intermediate or transition state which is unstable. The existence of only one real root shows that, for the particular values of pressure and temperature which give it, the substance can exist in only one state, either as a liquid or as a gas. The study of the real roots shows that, as the pressure and temperature increase, the values of the roots become more nearly equal, until for a certain definite pressure and temperature they become coincident; when the value of the temperature is still higher two of the roots cease to be real. The temperature which corresponds to the existence of three coincident roots is the critical temperature; at any temperature higher than that the substance can exist only as a gas.

224. General Explanation of Liquefaction, etc.—We will now apply the kinetic theory to give an explanation of the principal phenomena exhibited by a substance as it is heated. Let us consider a substance in the solid state at a temperature below its melting point; suppose heat applied to it gradually and at a uniform rate from some source. Its temperature will rise and it will in general expand; the rise of temperature is of course due to the increase in that part of the kinetic energy of the body which is the measure of temperature; on the view we have adopted, to the increase in the kinetic energy of molecular rotation or atomic vibration. The expansion is explained by the increase in the kinetic energy of translation, which enables the molecules to move farther from one another and so to increase the regions occupied by them. When the temperature rises to the melting-point, these regions have become so large that the molecules in them are no longer constrained to any definite directions; their motions