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:

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 ratio of the specific heats \(\frac{\mathbf{C}_{\mathrm{p}}}{\mathrm{C}_{\mathrm{v}}}=\gamma\) in terms of degrees of freedom(\(n\)) is given by:
1. \((1+\frac{1}{n})\)
2. \((1+\frac{n}{3})\)
3. \((1+\frac{2}{n})\)
4. \((1+\frac{n}{2})\)

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

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

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

The amount of heat energy required to raise the temperature of \(1\) g of Helium at NTP, from \(\mathrm{T_1}\) K to \(\mathrm{T_2}\) K is:
1. $\frac{3}{2}{\mathrm{N}}_{\mathrm{a}}{\mathrm{k}}_{\mathrm{B}}\left({\mathrm{T}}_2-{\mathrm{T}}_1\right)$

2. $\frac{3}{4}{\mathrm{N}}_{\mathrm{a}}{\mathrm{k}}_{\mathrm{B}}\left({\mathrm{T}}_2-{\mathrm{T}}_1\right)$

3. $\frac{3}{4}{\mathrm{N}}_{\mathrm{a}}{\mathrm{k}}_{\mathrm{B}}\frac{{\mathrm{T}}_2}{{\mathrm{T}}_1}$

4. $\frac{3}{8}{\mathrm{N}}_{\mathrm{a}}{\mathrm{k}}_{\mathrm{B}}\left({\mathrm{T}}_2-{\mathrm{T}}_1\right)$

If \(C_p\) and \(C_v\) denote the specific heats (per unit mass) of an ideal gas of molecular weight \(M\) (where \(R\) is the molar gas constant), the correct relation is:
1. \(C_p-C_v=R\)
2. \(C_p-C_v=\frac{R}{M}\)
3. \(C_p-C_v=MR\)
4. \(C_p-C_v=\frac{R}{M^2}\)

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. \(\frac{283}{383}x\)