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

1.	\(P_2>P_1\)	2.	\(P_2<P_1\)
3.	cannot be predicted	4.	\(P_2=P_1\)

The mean free path of molecules of a gas (radius \(r\)) is inversely proportional to:
1. \(r^3\)
2. \(r^2\) 
3. \(r\) 
4. \(\sqrt{r}\)

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:

Two vessels separately contain two ideal gases \(A\) and \(B\) at the same temperature, the pressure of \(A\) being twice that of \(B.\) Under such conditions, the density of \(A\) is found to be \(1.5\) times the density of \(B.\) The ratio of molecular weight of \(A\) and \(B\) is:

We have two vessels of equal volume, one filled with hydrogen and the other with equal mass of helium. The common temperature is \(27^{\circ}\text{C}.\) What is the relative number of molecules in the two vessels?
1. \(\frac{n_\mathrm{H}}{n_\mathrm{He}} = \frac{1}{1}\)
2. \(\frac{n_\mathrm{H}}{n_\mathrm{He}} = \frac{5}{1}\)
3. \(\frac{n_\mathrm{H}}{n_\mathrm{He}} = \frac{2}{1}\)
4. \(\frac{n_\mathrm{H}}{n_\mathrm{He}} = \frac{3}{1}\)

The volume \(V\) versus temperature \(T\) graph for a certain amount of a perfect gas at two pressures \(P_1\) and $$
\(P_2\) are shown in the figure. 

         
Here:

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. \(1.254\times 10^{4}~\text{K}\)

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:

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?
1. \(\frac{P}{kT}\)
2. \(\frac{Pm}{kT}\)
3. \(\frac{P}{kTV}\)
4. \(mkT\)