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

At a pressure of 24 × 10⁵ dyne/cm², the volume of O₂ is 10 litre and mass is 20g. The rms velocity will be:

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. \(\frac{n_H}{n_{He}} = \frac{3}{1}\)

During an experiment, an ideal gas is found to obey an additional law VP² = constant. The gas is initially at temperature T and volume V. What will be the temperature of the gas when it expands to a volume 2V?

1. $\mathrm{T}\text{'}=\sqrt{4}\mathrm{T}$

2. $\mathrm{T}\text{'}=\sqrt{2}\mathrm{T}$

3. $\mathrm{T}\text{'}=\sqrt{5}\mathrm{T}$

4. $\mathrm{T}\text{'}=\sqrt{6}\mathrm{T}$

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

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

The value of $C_P-C_v=1.00$ $R$ for a gas in state A and $C_P-C_v=1.06$ $R$ in another state B. If $P_A$ $and$ $P_B$ denote the pressure and $T_A \&$ $T_B$ denote the temperatures in the two states, then:

The volume and temperature graph is given in the figure below. If pressures for the two processes are different, then which one,  of the following, is true?

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. \(\frac{283}{383}x\)

The amount of heat energy required to raise the temperature of \(1\) g of Helium at NTP, from \({T_1}\) K to \({T_2}\) K is:
1. \(\frac{3}{2}N_ak_B(T_2-T_1)\)
2. \(\frac{3}{4}N_ak_B(T_2-T_1)\)
3. \(\frac{3}{4}N_ak_B\frac{T_2}{T_1}\)
4. \(\frac{3}{8}N_ak_B(T_2-T_1)\)

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: