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:

1.	\(\frac{2}{3}\)	2.	\(\frac{3}{4}\)
3.	\(2\)	4.	\(\frac{1}{2}\)

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 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. \(\frac{3}{8}N_ak_B(T_2-T_1)\)

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 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:

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 \(O_2\) and \(4\) moles of \(Ar\) at temperature \(T.\) Neglecting all the vibrational modes, the total internal energy of the system is:

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

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 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: