Consider a gas with density $\mathrm{\rho }$ and $\overline{\mathrm{c}}$ as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity v, then the pressure exerted by the gas is

1.  $\frac{1}{3}\mathrm{\rho }{\overline{\mathrm{c}}}^{ 2}$                                   

2.  $\frac{1}{3}\mathrm{\rho }{\left(\mathrm{c}+\mathrm{v}\right)}^2$

3.  $\frac{1}{3}\mathrm{\rho }{\left(\overline{\mathrm{c}}-\mathrm{v}\right)}^2$                         

4.  $\frac{1}{3}\mathrm{\rho }{\left({\mathrm{c}}^{-2}-\mathrm{v}\right)}^2$

In kinetic theory of gases, a molecule of mass m of an ideal gas collides with a wall of vessel with velocity V. The change in the linear momentum of the molecule is

1.  2mV                           

2.  mV

3.  – mV                           

4.  Zero

If the mean free path of atoms is doubled , then the pressure of gas will become

1. P/4                       

2. P/2

3. P/8                       

4. P

The ratio of mean kinetic energy of hydrogen and oxygen at a given temperature is

1.  1 : 16                     

2.  1 : 8

3.  1 : 4                       

4.  1 : 1

The average kinetic energy of a gas molecule can be determined by knowing

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

A sealed container with negligible coefficient of volumetric expansion contains helium (a monoatomic gas). When it is heated from 300 K to 600 K, the average K.E. of helium atoms is

1. Halved                     

2. Unchanged

3. Doubled                   

4. Increased by factor $\sqrt{2}$

The kinetic energy of translation of 20 gm of oxygen at 47°C is (molecular wt. of oxygen is 32 gm/mol and R = 8.3 J/mol/K)

1.  2490 joules                   

2.  2490 ergs

3.  830 joules                     

4.  124.5 joules

The kinetic energy of one gram molecules of a gas at standard temperature and pressure: $\left(\mathrm{R}=8.31 \mathrm{J}/\mathrm{mol}-\mathrm{K}\right)$

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

2.  $1.3\times {10}^2 \mathrm{J}$

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

4.  $3.4\times {10}^3 \mathrm{J}$

The mean kinetic energy of a gas at 300 K is 100 J. The mean energy of the gas at 450 K is equal to

1.  100 J                             

2.  3000 J

3.  450 J                             

4.  150 J

Read the given statements and decide which is/are correct on the basis of kinetic theory of gases

(I) Energy of one molecule at absolute temperature is zero

(II) r.m.s. speeds of different gases are same at same temperature

(III) For one gram of all ideal gas kinetic energy is same at same temperature

(IV) For one mole of all ideal gases, mean kinetic energy is same at same temperature

1. All are correct                         

2. I and IV are correct

3. IV is correct                           

4. None of these