of the substance when the volume is infinitely large, is strictly pv = MRT, where is a function of the volume v, absolute temperature T, and mass M in mols. The proof may be given an improved form which will now be pointed out. The term p(v-vi) in equation (3) may be written pv-pivi, where P, and pa denote the pressures in the condensed and vaporous states repectively. Equation (6), which applies to T = 0, may then be written Now (3) =0 at T0 (Phil. Mag. iv. p. 262, 1927), The rest of the argument is the same as before. The result may also be obtained independently of considerations of the zero of entropy. The writer has shown (J. Franklin Inst. 206 (5) p. 692, 1928) that a mon-atomic gas at infinite volume near in temperature to the absolute zero has a maximum specific heat whose value is abnormally large, which depends on the fact, deductable from Clapeyron's equation, that the internal heat of evaporation at T0 is zero. Thus the specific heat c, at constant volume is a function of the temperature, and this will therefore also hold for y, the ratio of the specific heats. Now the temperature scale of a perfect gas thermometer coincides with the thermodynamical scale of temperature only if y is a constant, and hence these scales strictly do not coincide. Therefore, if the temperature, as measured by the perfect gas thermometer, is expressed in terms of the temperature T on the thermodynamical scale, the equation of a perfect gas. becomes pv = RT. $(T'). It can now be shown similarly as before that the function. also involves the volume v. Yours faithfully, [The Editors do not hold themselves responsible for the views expressed by their correspondents.] |