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:

1.	\(\dfrac{P_1}{T_1}+\dfrac{P_2}{T_2}\)	2.	\(\dfrac{P_1T_1+P_2T_2}{(T_1+T_2)^2}\)
3.	\(\dfrac{P_1T_2+P_2T_1}{(T_1+T_2)^2}\)	4.	\(\dfrac{P_1}{2T_1}+\dfrac{P_2}{2T_2}\)

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 \(T_1\) and \(T_2.\) Which one, of the following, inferences is correct?

An ideal gas is initially at temperature T and volume V. Its volume increases by $∆\mathrm{V}$ due to an increase in temperature $∆\mathrm{T}$, pressure remaining constant. The quantity $\mathrm{\delta }=∆\mathrm{V}/\left(\mathrm{V}∆\mathrm{T}\right)$ varies with temperature as:

1.		2.
3.		4.

Which one, of the following, graphs represents the behaviour of an ideal gas at constant temperature?

1.		2.
3.		4.

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. \(0.768\)

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

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. \(a=b\)