Question

Calculate the KEper molecule and also r.m.s velocity of a gas at 127 ^oC.Given k_b =1.38 x 10 ^-23 J/molecule K& mass per molecule of the gas= 6.4x 10 ^-27kg

Answer 1

The kinetic energy per molecule is given by,
$$\begin{gathered} \frac{3}{2}\mathrm{kT}=\frac{3}{2}\times 1.38\times {10}^{-23}\times (273+127) \\ =\frac{3}{2}\times 1.38\times {10}^{-23}\times 400=8.28\times {10}^{-21}\mathrm{J} \\ \mathrm{Rms}\mathrm{velocity}, \\ {\mathrm{v}}_{\mathrm{r}.\mathrm{m}.\mathrm{s}}=\sqrt{\frac{2\mathrm{E}}{\mathrm{m}}} \\ =\sqrt{\frac{2\times 8.28\times {10}^{-21}}{6.4\times {10}^{-27}}}=\sqrt{2.58\times {10}^6}=1.6\times {10}^{3}m/s \end{gathered}$$