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 average kinetic energy of a helium atom at $30°C$ is:                                                                                           [MP PMT 2004]

1. Less than 1 eV

2. A few KeV

3. 50-60 eV

4. 13.6 eV

Choose the correct option related to the specific heat at constant volume $C_V$ -

1. $C_V=\frac{1}{2}fR$           

2. $C_V=\frac{R}{\gamma -1}$

3. $C_V=\frac{C_P}{\gamma }$               

4. All of these

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

1.		2.
3.		4.

Five molecules of a gas have speeds, 1, 2, 3, 4 and 5 km$s^{-1}$.  The value of the root mean square speed of the gas molecules is:

1. 3 km$s^{-1}$           

2. $\sqrt{11}$ km$s^{-1}$

3. $\frac{1}{2}\sqrt{\mathrm{\pi }}$ km$s^{-1}$   

4. 3.5 km$s^{-1}$

The average velocity of an ideal gas molecule is:

For a gas, $\frac{R}{C_V}=0.67$.  This gas is made up of molecules which are:                                                                   [JIPMER 2001, 02]

1. Diatomic           

2. Mixture of diatomic and polyatomic molecules

3. Monoatomic     

4. Polyatomic

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 %

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. \(1092~\text K\)