The molecules of a given mass of a gas have a r.m.s. velocity of 200 m/sec at 27°C and $1.0\times {10}^5 \mathrm{N}/{\mathrm{m}}^2$ pressure. When the temperature is 127°C and pressure is $0.5\times {10}^5 \mathrm{N}/{\mathrm{m}}^2,$ the r.m.s. velocity in m/sec will be

1. $\frac{100\sqrt{2}}{3}$                             

2. $100\sqrt{2}$

3. $\frac{400}{\sqrt{3}}$                                 

4. None of the above

Which of the following statement is true?

1. Absolute zero degree temperature is not zero energy temperature.

2. Two different gases at the same temperature pressure have equal root mean square velocities.

3. The root mean square speed of the molecules of different ideal gases, maintained at the same

    temperature are the same.

4. Given sample of 1 cc of hydrogen and 1 cc of oxygen both at NTP; oxygen sample has a large

    the number of molecules.

At which temperature the velocity of \(\mathrm{O_2}\) molecules will be equal to the velocity of \(\mathrm{N_2}\) molecules at \(0^\circ \text{C}?\)

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.  $1$