The pressure and temperature of two different gases are P and T with volume V for each.  If they are mixed, keeping the same volume and temperature, the pressure of the mixture will be:

If the mean free path of atoms is doubled then the pressure of the gas will become:
1. \(P/4\)           
2. \(P/2\)           
3. \(P/8\)           
4. \(P\)

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

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

1. 0.56 $\times {10}^4<mspace\; width="1em"></mspace>J$             

2. $1.3\times {10}^2<mspace\; width="1em"></mspace>J$

3. $2.7\times {10}^2<mspace\; width="1em"></mspace>J$                 

4. $3.4\times {10}^3<mspace\; width="1em"></mspace>J$

The molecular weight of two gases is \(M_1\) and \(M_2.\) At any temperature, the ratio of root mean square velocities \(v_1\) and \(v_2\) will be:
1. \(\sqrt{\frac{M_1}{M_2}}\)
2. \(\sqrt{\frac{M_2}{M_1}}\)
3. \(\sqrt{\frac{M_1+M_2}{M_1-M_2}}\)
4. \(\sqrt{\frac{M_1-M_2}{M_1+M_2}}\)

A gas mixture consist of 2 moles of $O_2$ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:

1. 4RT 

2. 15RT

3. 9RT

4. 11RT

One mole of an ideal monatomic gas undergoes a process described by the equation $P{V}^3=$ constant. The heat capacity of the gas during this process is:

1. $\frac{3}{2}R$           

2. $\frac{5}{2}R$

3. $2R$             

4. $R$

A given sample of an ideal gas occupies a volume V at a pressure p and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas?

1. p/(kT)        
2. pm / (kT)
3. p/ (kTV)     
4. mkT

The molecules of a given mass of gas have rms velocity of 200 ms^-1 at \(27^{\circ}\mathrm{C}\) and 1.0 x 10⁵ Nm^-2 pressure. When the temperature and pressure of the gas are increased to, respectively, \(127^{\circ}\mathrm{C}\) and 0.05 X 10⁵ Nm^-2, rms velocity of its molecules in ms^-1 will become:
1. 400/√3
2. 100√2/3
3. 100/3 
4.100√2