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. \(0.768\)

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

To find out the degree of freedom, the correct expression is:
1. \(f=\frac{2}{\gamma -1}\)
2. \(f=\frac{\gamma+1}{2}\)
3. \(f=\frac{2}{\gamma +1}\)
4. \(f=\frac{1}{\gamma +1}\)

A gas mixture consists of \(2\) moles of \(\mathrm{O_2}\) and \(4\) moles of \(\mathrm{Ar}\) at temperature \(T.\) Neglecting all the vibrational modes, the total internal energy of the system is:

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

A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at \(300\) K. The ratio of the average rotational kinetic energy per ${\mathrm{O}}_2$ molecule to that per ${\mathrm{N}}_2$ molecule is:

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

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. \(20~\text J\)

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: