Assertion: Equal moles of helium and oxygen gases are given equal quantities of heat at constant volume. There will be a greater rise in the temperature of helium as compared to that of oxygen.

Reason: The molecular weight of oxygen is more than the molecular weight of helium.

One mole of an ideal gas goes from an initial state $A$ to final state $B$ via two processes. It first undergoes isothermal expansion from volume $V$ to $3 V$ and then its volume is reduced from $3 V$ to $V$ at constant pressure. The correct $PV$ diagram representing the two processes is: 

In the given $(V-T)$ diagram, what is the relation between pressure $P_1$ and $P_2$?

A gas mixture consists of 2 moles of $\mathrm{O}_{2}$ and 4 moles of $\mathrm{Ar}$ at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system is 

At what temperature will the RMS speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? (Given: Mass of oxygen molecule $m=2.76\times {10}^{-26} \mathrm{kg}$, Boltzmann's constant $k_{\mathrm{B}}=1.38\times {10}^{-23} \mathrm{J} {\mathrm{K}}^{-1}$