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

The respective speeds of the molecules are 1, 2, 3, 4 and 5 km/sec. The ratio of their r.m.s. velocity and the average velocity will be

1. $\sqrt{11} \mathbf{:} 3$                                   

2. $3\mathbf{ }\mathbf{:} \sqrt{11}$

3. $1 \mathbf{:} 2$                                         

4. $3 \mathbf{:} 4$

Two vessels having equal volume contain molecular hydrogen at one atmosphere and helium at two atmospheres respectively. If both samples are at the same temperature, the mean velocity of hydrogen molecules is

1. Equal to that of helium                           

2. Twice that of helium

3. Half that of helium                                 

4. $\sqrt{2}$ times that of helium

According to the kinetic theory of gases the r.m.s. velocity of gas molecules is directly proportional to

1. $\mathrm{T}$                                 

2. $\sqrt{\mathrm{T}}$

3. ${\mathrm{T}}^2$                                 

4. $1/\sqrt{\mathrm{T}}$

At a given temperature the root mean square velocities of oxygen and hydrogen molecules are in the ratio

1.  16 : 1                               

2.  1 : 16

3.  4 : 1                                 

4.  1 : 4

The value of densities of two diatomic gases at constant temperature and pressure are ${\mathrm{d}}_1$ and ${\mathrm{d}}_2 ,$ then the ratio of the speed of sound in these gases will be :

1. ${\mathrm{d}}_1{\mathrm{d}}_2$                                   

2. $\sqrt{{\mathrm{d}}_2/{\mathrm{d}}_1}$

3. $\sqrt{{\mathrm{d}}_1/{\mathrm{d}}_2}$                             

4. $\sqrt{{\mathrm{d}}_1{\mathrm{d}}_2}$

By what factor the r.m.s. velocity will change, if the temperature is raised from 27°C to 327°C

1.  $\sqrt{2}$                                 

2.  $2$

3.  $2\sqrt{2}$                               

4.  $1$

At a given temperature if ${\mathrm{V}}_{\mathrm{rms}}$ is the root mean square velocity of the molecules of a gas and ${\mathrm{V}}_{\mathrm{s}}$ the velocity of sound in it, then these are related as $\left(\mathrm{\gamma }=\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{v}}}\right)$

1. ${\mathrm{V}}_{\mathrm{rms}}={\mathrm{V}}_{\mathrm{s}}$                             

2. ${\mathrm{V}}_{\mathrm{rms}}=\sqrt{\frac{3}{\mathrm{\gamma }}}\times {\mathrm{V}}_{\mathrm{s}}$

3. ${\mathrm{V}}_{\mathrm{rms}}=\sqrt{\frac{\mathrm{\gamma }}{3}}\times {\mathrm{V}}_{\mathrm{s}}$                   

4. ${\mathrm{V}}_{\mathrm{rms}}=\left(\frac{3}{\mathrm{\gamma }}\right)\times {\mathrm{V}}_{\mathrm{s}}$

For a gas at a temperature the root-mean-square velocity ${\mathrm{v}}_{\mathrm{rms}}$ , the most probable speed ${\mathrm{v}}_{\mathrm{mp}}$ , and the average speed ${\mathrm{v}}_{\mathrm{av}}$ obey the relationship

1. ${\mathrm{v}}_{\mathrm{av}}>{\mathrm{v}}_{\mathrm{rms}}>{\mathrm{v}}_{\mathrm{mp}}$                               

2. ${\mathrm{v}}_{\mathrm{rms}}>{\mathrm{v}}_{\mathrm{av}}>{\mathrm{v}}_{\mathrm{mp}}$

3. ${\mathrm{v}}_{\mathrm{mp}}>{\mathrm{v}}_{\mathrm{av}}>{\mathrm{v}}_{\mathrm{rms}}$                               

4. ${\mathrm{v}}_{\mathrm{mp}}>{\mathrm{v}}_{\mathrm{rms}}>{\mathrm{v}}_{\mathrm{av}}$