Equation of gas in terms of pressure (P), absolute temperature (T) and density (d) is :

1. $\frac{{\mathrm{P}}_1}{{\mathrm{T}}_1{\mathrm{d}}_1}=\frac{{\mathrm{P}}_2}{{\mathrm{T}}_2{\mathrm{d}}_2}$                                 

2. $\frac{{\mathrm{P}}_1{\mathrm{T}}_1}{{\mathrm{d}}_1}=\frac{{\mathrm{P}}_2{\mathrm{T}}_2}{{\mathrm{d}}_2}$

3. $\frac{{\mathrm{P}}_1{\mathrm{d}}_2}{{\mathrm{T}}_1}=\frac{{\mathrm{P}}_2{\mathrm{d}}_1}{{\mathrm{T}}_1}$                                 

4. $\frac{{\mathrm{P}}_1{\mathrm{d}}_1}{{\mathrm{T}}_1}=\frac{{\mathrm{P}}_2{\mathrm{d}}_2}{{\mathrm{T}}_2}$

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

The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K, the root mean square velocity of the gas molecules is v, at 480 K it becomes

1.  4v                                 

2.  2v

3.  v/2                               

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

Let A and B the two gases and given : $\frac{{\mathrm{T}}_{\mathrm{A}}}{{\mathrm{M}}_{\mathrm{A}}}=4.\frac{{\mathrm{T}}_{\mathrm{B}}}{{\mathrm{M}}_{\mathrm{B}}} ;$ where T is the temperature and M is molecular mass. If ${\mathrm{C}}_{\mathrm{A}}$ and ${\mathrm{C}}_{\mathrm{B}}$ are the r.m.s. speed, then the ratio $\frac{{\mathrm{C}}_{\mathrm{A}}}{{\mathrm{C}}_{\mathrm{B}}}$ will be equal to

1. 2                         

2. 4

3. 1                         

4. 0.5

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 \(1 \over 16\), then under constant pressure, the ratio of their rms velocities will be: