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

The r.m.s. speed of a group of 7 gas molecules having speeds $\left(6, 4, 2, 0, -2, -4, -6\right) \mathrm{m}/\mathrm{s}$ is

1. $1.5 \mathrm{m}/\mathrm{s}$                                   

2. $3.4 \mathrm{m}/\mathrm{s}$

3. $9 \mathrm{m}/\mathrm{s}$                                       

4. $4 \mathrm{m}/\mathrm{s}$

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

1. $\frac{4}{1}$                                   

2. $\frac{1}{4}$

3. $\frac{1}{16}$                                 

4. $\frac{16}{1}$

Molecular motion shows itself as

1. Temperature                     

2. Internal Energy

3. Friction                             

4. Viscosity

What is the velocity of wave in monoatomic gas having pressure 1 kilopascal and density $2.6 \mathrm{kg}/{\mathrm{m}}^3$ ?

1.  $3.6 \mathrm{m}/\mathrm{s}$                                 

2.  $8.9\times {10}^3 \mathrm{m}/\mathrm{s}$

3.  Zero                                       

4.  None of these

If the pressure in a closed vessel is reduced by drawing out some gas, the mean free path of the molecules:

At constant volume, temperature is increased. Then

1. Collision on walls will be less

2. Number of collisions per unit time will increase

3. Collisions will be in straight lines

4. Collisions will not change

The r.m.s. speed of a certain gas is n at 400K. The temperature at which the r.m.s. speed becomes two times, will be

1.  800 K                         

2.  1600 K

3.  1200 K                       

3.  None of these