The relation between two specific heats (in cal/mol) of a gas is:
1.  ${\mathrm{C}}_{\mathrm{P}}-{\mathrm{C}}_{\mathrm{V}}=\frac{\mathrm{R}}{\mathrm{J}}$                               

2.  ${\mathrm{C}}_{\mathrm{V}}-{\mathrm{C}}_{\mathrm{P}}=\frac{\mathrm{R}}{\mathrm{J}}$

3.  ${\mathrm{C}}_{\mathrm{P}}-{\mathrm{C}}_{\mathrm{V}}=\mathrm{J}$                                 

4.  ${\mathrm{C}}_{\mathrm{V}}-{\mathrm{C}}_{\mathrm{P}}=\mathrm{J}$

If the mean free path of atoms is doubled, then the pressure of the gas will become:

1. \(\frac{P}{4}\)                   
2. \(\frac{P}{2}\)
3. \(\frac{P}{8}\)
4. \(P\)

If \(V_\text{H}\),$$\(V_\text{N}\) and \(V_\text{O}\) denote the root-mean square velocities of molecules of hydrogen, nitrogen and oxygen respectively at a given temperature, then:
1. \(V_\text{N}>V_\text{O}>V_\text{H}\)
2. \(V_\text{H}>V_\text{N}>V_\text{O}\)
3. \(V_\text{O}>V_\text{N}>V_\text{H}\)
4. \(V_\text{O}>V_\text{H}>V_\text{N}\)

Two thermally insulated vessels \(1\) and \(2\) are filled with air at temperatures \(\mathrm{T_1},\) \(\mathrm{T_2},\) volume \(\mathrm{V_1},\) \(\mathrm{V_2}\) and pressure \(\mathrm{P_1},\) \(\mathrm{P_2}\) respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be:

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 pressure in a diatomic gas increases from ${\mathrm{P}}_0$ to $3{\mathrm{P}}_0$, when its volume is increased from ${\mathrm{V}}_0$ $\mathrm{to}$ $2{\mathrm{V}}_0$. The increase in internal energy  will be:
     
1. $6{\mathrm{P}}_{\mathrm{o}}{\mathrm{V}}_0$

2. $8.5{\mathrm{P}}_{\mathrm{o}}{\mathrm{V}}_0$

3. $12.5{\mathrm{P}}_{\mathrm{o}}{\mathrm{V}}_0$

4. $14.5{\mathrm{P}}_{\mathrm{o}}{\mathrm{V}}_0$

In the PV graph shown below for an ideal diatomic gas, the change in the internal energy is:
     

1. $\frac{3}{2}\mathrm{P}({\mathrm{V}}_2-{\mathrm{V}}_1)$

2. $\frac{5}{2}\mathrm{P}({\mathrm{V}}_2-{\mathrm{V}}_1)$

3. $\frac{3}{2}\mathrm{P}({\mathrm{V}}_1-{\mathrm{V}}_2)$

4. $\frac{7}{2}\mathrm{P}({\mathrm{V}}_1-{\mathrm{V}}_2)$

The figure shows a process for a gas in which pressure (P) and volume (V) of the gas change. If $C_1$ and $C_2$ are the molar heat capacities of the gas during the processes AB and BC respectively, then:

1. $C_1=C_2$

2. $C_1>C_2$

3. $C_1<C_2$

4. $C_1\le C_2$

The change in the internal energy of an ideal gas does not depend on?

The translational kinetic energy of oxygen molecules at room temperature is \(60~\text J.\) Their rotational kinetic energy will be?
1. \(40~\text J\)
2. \(60~\text J\)
3. \(50~\text J\)
4. \(20~\text J\)