The specific heat of an ideal gas is:

1.  proportional to $\mathrm{T.}$                     

2.  proportional to T².

3.  proportional to T³.                  

4.  independent of $\mathrm{T.}$

For hydrogen gas, the difference between molar specific heats is given by; \(C_P-C_V=a,\) and for oxygen gas, \(C_P-C_V=b.\) Here, \(C_P\)​ and \(C_V\)​ are molar specific heats expressed in \(\text{J mol}^{-1}\text{K}^{-1}.\) What is the relationship between \(a\) and \(b?\)
1. \(a=16b\)
2. \(b=16a\)
3. \(a=4b\)
4. \(a=b\)

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. \(0.768\)

An experiment is carried out on a fixed amount of gas at different temperatures and at high pressure such that it deviates from the ideal gas behaviour. The variation of $\frac{\mathrm{PV}}{\mathrm{RT}}$ with P is shown in the diagram. The correct variation will correspond to: (Assuming that the gas in consideration is nitrogen)

The figure below shows the graph of pressure and volume of a gas at two temperatures \(T_1\) and \(T_2.\) Which one, of the following, inferences is correct?

If the pressure in a closed vessel is reduced by drawing out some gas, the mean free path of the molecules:

At which temperature the velocity of \(\mathrm{O_2}\) molecules will be equal to the velocity of \(\mathrm{N_2}\) molecules at \(0^\circ \text{C}?\)

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:

At \(10^{\circ}\text{C}\) the value of the density of a fixed mass of an ideal gas divided by its pressure is \(x.\) At \(110^{\circ}\text{C}\) this ratio is:

The ratio of the specific heats \(\frac{C_P}{C_V}=\gamma\) in terms of degrees of freedom \((n)\) is given by:
1. \(1+1/n\)
2. \(1+n/3\)
3. \(1+2/n\)
4. \(1+n/2\)