An ideal gas undergoes a process maintaining relation between pressure $(P)$ and $\operatorname{volume}(V)$ as $P=P_{\mathrm{o}}\left(1+\left(\frac{V_{\mathrm{o}}}{V}\right)^2\right)^{-1}$, where $P_{\mathrm{o}}$ and $V_{\mathrm{o}}$ are constants. If two samples $A$ and $B$ (two moles each) with initial volumes $V_{\mathrm{o}}$ and $3 V_{\mathrm{o}}$ respectively undergo above mentioned process and attain same pressure, then the difference at the temperatures of these samples, $T_B-T_A$ is $\_\_\_\_$ .

( $R=$ gas constant)

A mixture of carbon dioxide and oxygen has volume 8310 cm³, temperature 300 K, pressure 100 kPa and mass 13.2 g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are ______.

(Assume both carbon dioxide and oxygen gases behave like ideal gases) [R = 8.31 J/mol K]

Heat is supplied to a diatomic gas at constant pressure. Then the ratio of $\Delta Q : \Delta U : \Delta W$ is ______.

The mean free path of a molecule of diameter $5 \times 10^{-10}$ m at the temperature $41^{\circ}$C and pressure $1.38 \times 10^5$ Pa, is given as ________ m. (Given $k_B = 1.38 \times 10^{-23}$ J/K).