 n R T = \displaystyle \frac{1}{3} N m \langle u^2 \rangle\\ \\ n R T = \displaystyle \frac{1}{3} n N_{\rm A} m \langle u^2 \rangle\\ \\ \displaystyle \frac{1}{2} N_{\rm A} m \langle u^2 \rangle = \frac{3}{2} RT 