The specific heat of an ideal gas is:

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

2.  proportional to T².

3.  proportional to T³.                  

4.  independent of $\mathrm{T.}$

The specific heat of a gas:

For hydrogen gas \(C_P-C_V=a\) and for oxygen gas \(C_P-C_V=b\) where molar specific heats are given. So the relation between \(a\) and \(b\) is given by: (where \(C_p\) and \(C_V\) in J mol^-1 K^-1)
1. \(a=16b\)
2. \(b=16a\)
3. \(a=4b\)
4. \(a=b\)

The translatory kinetic energy of a gas per \(\text{g}\) is:

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. \(0.768\)

Two containers of equal volumes contain the same gas at pressures \(P_1\)${\mathrm{}}_{}$ and \(P_2\)${\mathrm{}}_{}$ and absolute temperatures \(T_1\)${\mathrm{}}_{}$ and \(T_2\)${\mathrm{}}_{}$, respectively. On joining the vessels, the gas reaches a common pressure \(P\) and common temperature \(T\). The ratio \(\frac{P}{T}\) is equal to:
1. \(\frac{P_1}{T_1}+\frac{P_2}{T_2}\)
2. \(\frac{P_1T_1+P_2T_2}{(T_1+T_2)^2}\)
3. \(\frac{P_1T_2+P_2T_1}{(T_1+T_2)^2}\)
4. \(\frac{P_1}{2T_1}+\frac{P_2}{2T_2}\)

The root mean square speed of the molecules of a diatomic gas is \(v\). When the temperature is doubled, the molecules dissociate into two atoms. The new root mean square speed of the atom is:

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:

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 ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$. Which one, of the following, inferences is correct?