The volume \(V\) versus temperature \(T\) graph for a certain amount of a perfect gas at two pressures \(\mathrm{P}_1\) and $$
\(\mathrm{P}_2\) are shown in the figure. Here:

  

1.	\(\mathrm{P}_1<\mathrm{P}_2\)
2.	\(\mathrm{P}_1>\mathrm{P}_2\)
3.	\(\mathrm{P}_1=\mathrm{P}_2\)
4.	Pressures can’t be related

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

The ratio of ${\mathrm{v}}_{\mathrm{rms}}:{\mathrm{v}}_{\mathrm{mp}}:{\mathrm{v}}_{\mathrm{avg}}$ is: (symbols have their usual meaning)

$1. \sqrt{3}:\sqrt{2}:\sqrt{\frac{\mathrm{\pi }}{8}}$
$2. \sqrt{3}:\sqrt{2}:\sqrt{\frac{8}{3}}$
$3. \sqrt{3}:\sqrt{\frac{8}{\mathrm{\pi }}}:\sqrt{2}$
$4. \sqrt{3}:\sqrt{2}:\sqrt{\frac{8}{\mathrm{\pi }}}$

At \(10^{\circ}\mathrm{C}\) the value of the density of a fixed mass of an ideal gas divided by its pressure is \(x\). At \(110^{\circ}\mathrm{C}\) this ratio is:
1. \(x\)
2. \(\frac{383}{283}x\)
3. \(\frac{10}{110}x\)
4. \(\frac{283}{383}x\)

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

The root mean square velocity of the molecules of a gas is 300 m/s. What will be the root mean square speed of the molecules if the atomic weight is doubled and absolute temperature is halved?

The rms speed of oxygen atoms is v. If the temperature is halved and the oxygen atoms combine to form oxygen molecules, then the rms speed will be:

1. $\frac{v}{\sqrt{2}}$

2. $v\sqrt{2}$

3. 2v

4. $\frac{v}{2}$

The figure below shows the graph of pressure and volume of a gas at two temperatures ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$. Which one, of the following, inferences is correct?

An experiment is carried out on a fixed amount of gas at different temperatures and at high pressure such that it deviates from the ideal gas behaviour. The variation of $\frac{\mathrm{PV}}{\mathrm{RT}}$ with P is shown in the diagram. The correct variation will correspond to: (Assuming that the gas in consideration is nitrogen)

The average translational kinetic energy of \(O_2\) (molar mass \(32\)) molecules at a particular temperature is \(0.048~\text{eV}\). The translational kinetic energy of \(N_2\) (molar mass \(28\)) molecules in \(\text{eV}\) at the same temperature is:
1. \(0.0015\)
2. \(0.003\)
3. \(0.048\)
4. \(0.768\)