A diatomic molecule has how many degrees of freedom-                                                                                             

(1) 3            (2) 4           (3) 5              (4) 6

Mean kinetic energy per degree of freedom of gas molecules is:

1. $\frac{3}{2}kT$             

2. kT             

3. $\frac{1}{2}kT$             

4. $\frac{3}{2}RT$

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

The degrees of freedom of a triatomic gas is

1.  2                                 

2.  4

3.  6                                 

3.  8

The number of translational degrees of freedom for a diatomic gas is

1.  2                           

2.  3

3.  5                           

4.  6

Two ideal gases at absolute temperature ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ are mixed. There is no loss of energy. The masses of the molecules are ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ and the number of molecules in the gases are ${\mathrm{n}}_1$ and ${\mathrm{n}}_2$ respectively. The temperature of mixture will be

1. $\frac{{\mathrm{T}}_1+{\mathrm{T}}_2}{2}<mspace\; width="1em"></mspace>\mathrm{energy}$                     

2. $\frac{{\mathrm{T}}_1+{\mathrm{T}}_2}{{\mathrm{n}}_1{\mathrm{n}}_2}$

3. $\frac{{\mathrm{n}}_1{\mathrm{T}}_1+{\mathrm{n}}_2{\mathrm{T}}_2}{{\mathrm{n}}_1+{\mathrm{n}}_2}$                         

4. $\left({\mathrm{T}}_1+{\mathrm{T}}_2\right)$

A vessel contains a mixture of one mole of oxygen and two moles of nitrogen at \(300\) K. The ratio of the average rotational kinetic energy per ${\mathrm{O}}_2$ molecule to that per ${\mathrm{N}}_2$ molecule is:

One mole of an ideal diatomic gas undergoes a transition from \(A\) to \(B\) along a path \(AB\) as shown in the figure. 
         
The change in internal energy of the gas during the transition is:

Assertion The molecules of a monoatomic gas have three degrees of freedom. 

Reason The molecules of a diatomic gas have five degrees of freedom.