Statistical Mechanics · Problem 1.7

Elements of Ensemble Theory — R. K. Pathria

Physics — Statistical Mechanics · ultra-relativistic-ideal-gas

Problem

Study the statistical mechanics of an extreme relativistic gas characterized by the single-particle energy states

\varepsilon(n_x, n_y, n_z) = \frac{hc}{2L}(n_x^2 + n_y^2 + n_z^2)^{1/2},

instead of (1.4.5), along the lines followed in Sec. 1.4. Show that the ratio

C_P/C_V

in this case is

4/3

, instead of

5/3