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:

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 %

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]

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

By what percentage, should the pressure of a given mass of gas be increased, so as to decrease its volume by 10% at a constant temperature?

1. 5%     

2. 7.2 %       

3. 12.5%         

4. 11.1%

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

1.		2.
3.		4.

The root-mean-square velocity of the molecules in a sample of helium is $\frac{5}{7}th$ of that of the molecules in a sample of hydrogen.  If the temperature of the hydrogen gas is 0$°$C, that of the helium sample is about:

1. 0$°$C       

2. 5.6$°$C      

3. 273$°$C         

4. 100$°$C

The kinetic energy of one gram molecule of a gas at standard temperature and pressure is: (R = 8.31 J/mol-K)

1. 0.56 $\times {10}^4 J$             

2. $1.3\times {10}^2 J$

3. $2.7\times {10}^2 J$                 

4. $3.4\times {10}^3 J$