An isolated system-

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. \(P\)

Which of the following relations is correct for the root-mean-square speed of gas at temperature T?

Where, k= Boltzmann constant, and m= mass of a molecule.

(1) $V_{r.m.s}=\sqrt{\frac{3 k\hspace{0.17em}T}{m}}$   

(2)$V_{r.m.s}=\sqrt{\frac{8 k\hspace{0.17em}T}{m \mathrm{\pi }}}$

(3) $V_{r.m.s}=\sqrt{\frac{2 k\hspace{0.17em}T}{m}}$   

(4) $V_{r.m.s}=\sqrt{\frac{m}{3 k T}}$

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

The mean translational kinetic energy of a perfect gas molecule at the temperature T Kelvin is:

1. $\frac{1}{2}kT$         

2. kT             

3. $\frac{3}{2}kT$           

4. 2 kT

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:

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