The molecules of a given mass of gas have rms velocity of 200 ms^-1 at \(27^{\circ}\mathrm{C}\) and 1.0 x 10⁵ Nm^-2 pressure. When the temperature and pressure of the gas are increased to, respectively, \(127^{\circ}\mathrm{C}\) and 0.05 X 10⁵ Nm^-2, rms velocity of its molecules in ms^-1 will become:
1. 400/√3
2. 100√2/3
3. 100/3 
4.100√2

A given sample of an ideal gas occupies a volume \(V\) at a pressure \(P\) and absolute temperature \(T\). The mass of each molecule of the gas is \(m\). Which of the following gives the density of the gas?
1. \(\frac{P}{kT}\)
2. \(\frac{Pm}{kT}\)
3. \(\frac{P}{kTV}\)
4. \(mkT\)

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:

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:

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:

The mean free path of molecules of a gas (radius \(r\)) is inversely proportional to:
1. \(r^3\)
2. \(r^2\) 
3. \(r\) 
4. \(\sqrt{r}\)

In the given \({(V\text{-}T)}\) diagram, what is the relation between pressure \({P_1}\) and \({P_2}\)? 
              

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: