$V_{rms},V_{av},V_{mp}$ 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

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

1.		2.
3.		4.

The root-mean-square (RMS) speed of oxygen molecules $\left(O_2\right)$ at a certain absolute temperature is v. If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the RMS speed would be:

1. V                       

2. $\sqrt{2}v$

3. 2 v                     

4. 2 $\sqrt{2}v$

At what temperature is the root mean square speed of molecules of hydrogen twice as that at STP?
1. $273~\text K$
2. $546~\text K$ 
3. $819~\text K$ 
4. $1092~\text K$ 

Volume, pressure, and temperature of an ideal gas are $V,$ $P,$ and $T$ respectively. If the mass of its molecule is $m,$ then its density is:
[$k$=Boltzmann's constant]

In the adjacent V-T diagram, what is the relation between $P_{1 }and P_2$ ?

1. $P_2=P_1$                               

2. $P_2>P_1$

3. $P_2<P_1$                                 

4. cannot be predicated
 

Which one of the following graph is correct at constant pressure?

1.		2.
3.		4.

The equation $\left(p+\frac{a}{v^2}\right)\left(v-b\right)=RT$ is known as:

1. Perfect gas equation

2. Joule Thomson's equation

3. Vander Waal's equation

4. Maxwell's equation