At a pressure of \(24\times 10^{5}~\text{dyne/cm}^2\), the volume of \(O_2\) is \(10\) litre and mass is \(20\text{g}\). The rms velocity will be:

1.	\(800~\text{m/s}\)	2.	\(400~\text{m/s}\)
3.	\(600~\text{m/s}\)	4.	Data is incomplete.

The ratio of ${\mathrm{v}}_{\mathrm{rms}}:{\mathrm{v}}_{\mathrm{mp}}:{\mathrm{v}}_{\mathrm{avg}}$ is: (symbols have their usual meaning)

$1. \sqrt{3}:\sqrt{2}:\sqrt{\frac{\mathrm{\pi }}{8}}$
$2. \sqrt{3}:\sqrt{2}:\sqrt{\frac{8}{3}}$
$3. \sqrt{3}:\sqrt{\frac{8}{\mathrm{\pi }}}:\sqrt{2}$
$4. \sqrt{3}:\sqrt{2}:\sqrt{\frac{8}{\mathrm{\pi }}}$

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?

The volume \(V\) versus temperature \(T\) graph for a certain amount of a perfect gas at two pressures \(P_1\) and $$
\(P_2\) are shown in the figure. 

         
Here:

We have two vessels of equal volume, one filled with hydrogen and the other with equal mass of helium. The common temperature is \(27^{\circ}\text{C}.\) What is the relative number of molecules in the two vessels?
1. \(\frac{n_\mathrm{H}}{n_\mathrm{He}} = \frac{1}{1}\)
2. \(\frac{n_\mathrm{H}}{n_\mathrm{He}} = \frac{5}{1}\)
3. \(\frac{n_\mathrm{H}}{n_\mathrm{He}} = \frac{2}{1}\)
4. \(\frac{n_\mathrm{H}}{n_\mathrm{He}} = \frac{3}{1}\)

During an experiment, an ideal gas is found to obey an additional law VP² = constant. The gas is initially at temperature T and volume V. What will be the temperature of the gas when it expands to a volume 2V?

1. $\mathrm{T}\text{'}=\sqrt{4}\mathrm{T}$

2. $\mathrm{T}\text{'}=\sqrt{2}\mathrm{T}$

3. $\mathrm{T}\text{'}=\sqrt{5}\mathrm{T}$

4. $\mathrm{T}\text{'}=\sqrt{6}\mathrm{T}$

The value of $C_P-C_v=1.00$ $R$ for a gas in state A and $C_P-C_v=1.06$ $R$ in another state B. If $P_A$ $and$ $P_B$ denote the pressure and $T_A \&$ $T_B$ denote the temperatures in the two states, then:

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?

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:

The amount of heat energy required to raise the temperature of \(1\) g of Helium at NTP, from \({T_1}\) K to \({T_2}\) K is:
1. \(\frac{3}{2}N_ak_B(T_2-T_1)\)
2. \(\frac{3}{4}N_ak_B(T_2-T_1)\)
3. \(\frac{3}{4}N_ak_B\frac{T_2}{T_1}\)
4. \(\frac{3}{8}N_ak_B(T_2-T_1)\)