The average energy of a molecule for each degree of freedom is:

1.	\(\dfrac{3}{2} kT\)	2.	\(\dfrac{kT}{2}\)
3.	\(\dfrac{3}{4} kT\)	4.	\(kT\)

A given sample of an ideal gas occupies a volume \(V\) at a pressure \(P\) and absolute temperature \(T\). The mass of each molecule of the gas is \(m\). Which of the following gives the density of the gas?

A gas mixture consists of \(2\) moles of \(\mathrm{O_2}\) and \(4\) moles of \(\mathrm{Ar}\) at temperature \(T.\) Neglecting all the vibrational modes, the total internal energy of the system is:

At what temperature will the \(\text{rms}\) speed of oxygen molecules become just sufficient for escaping from the earth's atmosphere? 
(Given: Mass of oxygen molecule \((m)= 2.76\times 10^{-26}~\text{kg}\), Boltzmann's constant \(k_B= 1.38\times10^{-23}~\text{J K}^{-1}\))
1. \(2.508\times 10^{4}~\text{K}\)
2. \(8.360\times 10^{4}~\text{K}\)
3. \(5.016\times 10^{4}~\text{K}\)
4. \(1.254\times 10^{4}~\text{K}\)

\(4.0~\text{gm}\) of gas occupies \(22.4~\text{litres}\) at NTP. The specific heat capacity of the gas at a constant volume is  \(5.0~\text{JK}^{-1}\text{mol}^{-1}.\) If the speed of sound in the gas at NTP is \(952~\text{ms}^{-1},\) then the molar heat capacity at constant pressure will be:
(\(R=8.31~\text{JK}^{-1}\text{mol}^{-1}\)) 

One mole of an ideal diatomic gas undergoes a transition from \(A\) to \(B\) along a path \(AB\) as shown in the figure. 
         
The change in internal energy of the gas during the transition is:

The mean free path of molecules of a gas (radius \(r\)) is inversely proportional to:

In the given \({(V\text{-}T)}\) diagram, what is the relation between pressure \({P_1}\) and \({P_2}\)?