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. \(1092~\text K\) 

At what temperature, is the root mean square velocity of gaseous hydrogen molecules equal to that of oxygen molecules at 47$°$C:[MP PET 1997, 2000; RPET 1999; AIEEE 2002; J & K CET 2004; Kerala PET 2010]

1. 20 K           

2. 80 K           

3. - 73 K             

4. 3 K

The average kinetic energy of a gas molecule can be determined by knowing:                                        [RPET 2000, MP PET 2010]

1. The number of molecules in the gas

2. The pressure of the gas only

3. The temperature of the gas only

4. None  of the above is enough by itself

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]