$V_{rms},V_{av},V_{mp}$ are root mean square, average and most probable speeds of molecules of a gas obeying Maxwellian velocity distribution. Which of the following statements is correct?

1. $V_{rms}<V_{av}<V_{mp}$

2. $V_{rms}>V_{av}>V_{mp}$

3. $V_{rms} < V_{av}>V_{mp}$

4. $V_{avg}>V_{rms}<V_{mp}$

Gas is found to obey the law $P^{2}V$ = constant. The initial temperature and volume are $T_0$ and $V_0$. If the gas expands to a volume $3V_0$, its final temperature becomes:

1. $\frac{T_0}{3}$           

2. $\frac{T_0}{\sqrt{3}}$

3. $3T_0$           

4. None of these

For a gas, the r.m.s speed at 800 K is:

1. Four times the value at 200 K

2. Half the value at 200 K

3. Twice the value at 200 K

4. Same as at 200 K

The mean translational kinetic energy of a perfect gas molecule at the temperature T Kelvin is:

1. $\frac{1}{2}kT$         

2. kT             

3. $\frac{3}{2}kT$           

4. 2 kT

The curve between absolute temperature and \(\mathrm{v}^2_{rms}\)${\mathrm{}}^{}$ is:

1.		2.
3.		4.

At constant temperature, on increasing the pressure of a gas by 5% , its volume will decrease by:          

1. 5%       

2. 5.26 %         

3. 4.26 %         

4. 4.76 %

One liter of gas A and two liters of gas B, both having the same temperature 100$°$C and the same pressure 2.5 bar will have the ratio of average kinetic energies of their molecules as:

1. 1:1       

2. 1:2     

3. 1:4       

4. 4:1

Four molecules have speeds 2 km/sec, 3 km/sec, 4 km/sec and 5 km/sec.  The root mean square speed of these molecules (km/sec) is:

1. $\sqrt{\frac{54}{4}}$       

2. $\sqrt{\frac{54}{2}}$         

3. 3.5           

4. 3$\sqrt{3}$

For gas, if the ratio of specific heats at constant pressure p and constant volume V is ${\rm Y}$, then value of degree of freedom is:

1. $\frac{\gamma +1}{\gamma -1}$           

2. $\frac{\gamma -1}{\gamma +1}$           

3. $\frac{\gamma -1}{2}$           

4. $\frac{2}{\gamma -1}$

Gases exert pressure on the walls of containing vessel because  the gas molecules:

1. Possess momentum

2. collide with each other

3. have finite volume

4. obey gas laws