The root mean square velocity of the molecules of a gas is \(300 ~\text{m/s}.\) What will be the root mean square speed of the molecules if the atomic weight is doubled and the absolute temperature is halved?

1.	\(300 ~\text{m/s}\)	2.	\(150 ~\text{m/s}\)
3.	\(600 ~\text{m/s}\)	4.	\(75 ~\text{m/s}\)

Two chambers of different volumes, one containing ${\mathrm{m}}_1$g of a gas at pressure ${\mathrm{P}}_1$ and other containing ${\mathrm{m}}_2$g of the same gas at pressure ${\mathrm{P}}_2$ are joined to each other. If the temperature of the gas remains constant, the common pressure reached is:

1.  $\frac{{\mathrm{m}}_1{\mathrm{P}}_1+{\mathrm{m}}_2{\mathrm{P}}_2}{{\mathrm{m}}_1<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>{\mathrm{m}}_2}$

2.  $\frac{{\mathrm{m}}_1{\mathrm{P}}_2+{\mathrm{m}}_2{\mathrm{P}}_1}{{\mathrm{m}}_1<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>{\mathrm{m}}_2}$

3.  $\frac{{\mathrm{m}}_1{\mathrm{P}}_2+\left({\mathrm{P}}_1+{\mathrm{P}}_2\right)}{{{\mathrm{m}}^2}_1<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>{\mathrm{m}}_2}$

4.  $\frac{\left({\mathrm{m}}_1+{\mathrm{m}}_2\right){\mathrm{P}}_1{\mathrm{P}}_2}{{\mathrm{m}}_1{\mathrm{P}}_2<mspace\; width="1em"></mspace>+<mspace\; width="1em"></mspace>{\mathrm{m}}_2{\mathrm{P}}_1}$

The rms speed of oxygen atoms is v. If the temperature is halved and the oxygen atoms combine to form oxygen molecules, then the rms speed will be:

1. $\frac{v}{\sqrt{2}}$

2. $v\sqrt{2}$

3. 2v

4. $\frac{v}{2}$

Two thermally insulated vessels \(1\) and \(2\) are filled with air at temperatures \(\mathrm{T_1},\) \(\mathrm{T_2},\) volume \(\mathrm{V_1},\) \(\mathrm{V_2}\) and pressure \(\mathrm{P_1},\) \(\mathrm{P_2}\) respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be:

If \(V_\text{H}\),$$\(V_\text{N}\) and \(V_\text{O}\) denote the root-mean square velocities of molecules of hydrogen, nitrogen and oxygen respectively at a given temperature, then:
1. \(V_\text{N}>V_\text{O}>V_\text{H}\)
2. \(V_\text{H}>V_\text{N}>V_\text{O}\)
3. \(V_\text{O}>V_\text{N}>V_\text{H}\)
4. \(V_\text{O}>V_\text{H}>V_\text{N}\)

If the ratio of vapour density for hydrogen and oxygen is \(\frac{1}{16},\) then under constant pressure, the ratio of their RMS velocities will be:

If the mean free path of atoms is doubled, then the pressure of the gas will become:

1. \(\frac{P}{4}\)                   
2. \(\frac{P}{2}\)
3. \(\frac{P}{8}\)
4. \(P\)

The relation between two specific heats (in cal/mol) of a gas is:
1.  ${\mathrm{C}}_{\mathrm{P}}-{\mathrm{C}}_{\mathrm{V}}=\frac{\mathrm{R}}{\mathrm{J}}$                               

2.  ${\mathrm{C}}_{\mathrm{V}}-{\mathrm{C}}_{\mathrm{P}}=\frac{\mathrm{R}}{\mathrm{J}}$

3.  ${\mathrm{C}}_{\mathrm{P}}-{\mathrm{C}}_{\mathrm{V}}=\mathrm{J}$                                 

4.  ${\mathrm{C}}_{\mathrm{V}}-{\mathrm{C}}_{\mathrm{P}}=\mathrm{J}$

The volume and temperature graph is given in the figure below. If pressures for the two processes are different, then which one,  of the following, is true?