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

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:

What is the velocity of a wave in a 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

1. Is decreased

2. Is increased

3. Remains unchanged

4. Increases or decreases according to the nature of the gas

At constant volume, for different diatomic gases the molar specific heat is

1. Same and 3 cal/mole/°C approximately

2. Exactly equal and its value is 4 cal/mole/°C

3. Will be totally different

4. Approximately equal and its value is 5 cal/mole/°C

The specific heats at constant pressure is greater than that of the same gas at constant volume because

1. At constant pressure work is done in expanding the gas

2. At constant volume work is done in expanding the gas

3. The molecular attraction increases more at constant pressure

4. The molecular vibration increases more at constant pressure

Gas at a pressure ${\mathrm{P}}_0$ is contained in a vessel. If the masses of all the molecules are halved and their speeds are doubled, the resulting pressure P will be equal to

1.  $4{\mathrm{P}}_0$                                 

2.  $2{\mathrm{P}}_0$

3.  ${\mathrm{P}}_0$                                   

4.  $\frac{{\mathrm{P}}_0}{2}$

Consider a gas with density $\mathrm{\rho }$ and $\overline{\mathrm{c}}$ as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity v, then the pressure exerted by the gas is

1.  $\frac{1}{3}\mathrm{\rho }{\overline{\mathrm{c}}}^{ 2}$                                   

2.  $\frac{1}{3}\mathrm{\rho }{\left(\mathrm{c}+\mathrm{v}\right)}^2$

3.  $\frac{1}{3}\mathrm{\rho }{\left(\overline{\mathrm{c}}-\mathrm{v}\right)}^2$                         

4.  $\frac{1}{3}\mathrm{\rho }{\left({\mathrm{c}}^{-2}-\mathrm{v}\right)}^2$

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. \(P\)

A sealed container with negligible coefficient of volumetric expansion contains helium (a monoatomic gas). When it is heated from 300 K to 600 K, the average K.E. of helium atoms is

1. Halved                     

2. Unchanged

3. Doubled                   

4. Increased by factor $\sqrt{2}$