Problem 2.86

In the case of gaseous nitrogen find: (a) the temperature at which the velocities of the molecules $v_{1}$ $=300 \mathrm{~m} / \mathrm{s}$ and $v_{2}=600 \mathrm{~m} / \mathrm{s}$ are associated with equal values of the Maxwell distribution function $F(v)$ (b) the velocity of the molecules $v$ at which the value of the Maxwell distribution function $F(v)$ for the temperature $T_{0}$ will be the same as that for the temperature $\eta$ times higher.

\text { (a) } T=\frac{m\left(v_{2}^{2}-v_{1}^{2}\right)}{4 k \ln \left(v_{2} / v_{1}\right)}=330 \mathrm{~K} \text { (b) } v=\sqrt{\frac{3 k T_{0}}{m} \frac{\eta \ln \eta}{\eta-1}}

Kinetic theory of gases. Boltzmanns Law and Maxwell distribution