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

1.	\(40^\circ \text{C}\)	2.	\(93^\circ \text{C}\)
3.	\(39^\circ \text{C}\)	4.	Cannot be calculated

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

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, 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 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 \(P_2\) and absolute temperatures \(T_1\) and \(T_2\), respectively. On joining the vessels, the gas reaches a common pressure \(P\) and common temperature \(T\). The ratio \(\dfrac{P}{T}\) is equal to:

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: