140.

equal to N k for T = ∞ . A. EinsteinA. Einstein, Ann. d. Phys. 22, p. 180, 1907. Compare also M. Born und Th. von Kárman, Phys. Zeitschr. 13, p. 297, 1912. has made an important application of this equation to the heat capacity of solid bodies, but a closer discussion of this would be beyond the scope of the investigations to be made in this book.

For the constants $\alpha$ and $\gamma$ in the expression [eqn:(220)] (220) for the distribution density $w$ we find from [eqn:(221)] (221): $\alpha =e^{\frac{h\nu }{kT}}-1\gamma =e^{-\frac{h\nu }{kT}}\mathrm{\backslash Label}[eqn](227)\text{upshape (227)}$ and finally for the entropy $S$ of our system as a function of temperature: $S=kN\{\frac{{\displaystyle \frac{h\nu }{kT}}}{e^{\frac{h\nu }{kT}-1}}-\log (1-e^{-\frac{h\nu }{kT}})\}.\mathrm{\backslash Label}[eqn](228)\text{upshape (228)}$

[Direct Calculation of the Entropy] IVDirect Calculation of the Entropy in The Case of Thermodynamic Equilibrium