Compute the mean translational kinetic energy of (a) a single ideal gas molecule in eV, and (b) a mole of ideal gas in J, both at room temperature 293 K.
Strategy The mean kinetic energy of a single molecule is given by Equation (9.8). For an entire mole, it’s necessary to multiply the result by Avogadro’s number N_{A}, the number of atoms in a mole.
\overline{K}=\frac{\overline{1m v^{2}} }{2}=\frac{1}{2} m\left(\overline{v_{x}^{2}}+\overline{v_{y}^{2}}+\overline{v_{z}^{2}}\right)=\frac{1}{2} m\left(\frac{3 k T}{m}\right)=\frac{3}{2} k T (9.8)