The average translational kinetic energy of - nitrogen (molar mass 28) molecules at a particular temperature…

The average translational kinetic energy of - nitrogen (molar mass 28) molecules at a particular temperature is 0.042 eV . The translational kinetic energy of oxygen molecules (molar mass 32 ) in eV at double the temperature is
  1. 0.021
  2. 0.048
  3. 0.056
  4. 0.084

Solution

$\mathrm{E}_{\left(\mathrm{N}_2\right)}=0.042 \mathrm{eV}$
Translational Kinetic Energy is given by, $\begin{array}{ll} & E=\frac{3}{2} k T \\ \therefore & E \propto T \\ \therefore & \frac{E_{\left(N_2\right)}}{E_{\left(O_2\right)}}=\frac{T_1}{T_2} \\ \therefore & \frac{0.042}{E_{\left(O_2\right)}}=\frac{T}{2 T} \\ \therefore & E_{\left(O_2\right)}=0.084 \mathrm{eV} \end{array}$

Asked in: MHT CET 2024 (02 May Shift 2)

Practice more Kinetic Theory of Gases and Radiation questions on Aicharya