134.

To this we may at once add another quantitative relation. All the preceding calculations rest on the assumption that the distribution density $w$ and hence also the constant $\alpha$ in [eqn:(183)] (183) are small ([sect:129.] Sec. 129). Hence, if we take the value of $\alpha$ from [eqn:(184)] (184) and take account of [eqn:(188)] (188), [eqn:(189)] (189) and [eqn:(201)] (201), it follows that $\frac{p}{T^{\frac{5}{2}}}{e}^{-\frac{a}{R}-1}\text{must be small.}$ When this relation is not satisfied, the gas cannot be in the ideal state. For the saturated vapor it follows then from [eqn:(202)] (202) that $e^{-\frac{A{r}_0}{RT}}$ is small. In order, then, that a saturated vapor may be assumed to be in the state of an ideal gas, the temperature $T$ must certainly be less than ${\displaystyle \frac{A}{R}}{r}_0$ or ${\displaystyle \frac{r_0}{2}}$. Such a restriction is unknown to the classical thermodynamics.