At constant volume the specific heat of a gas is 3R/2, then the value of γ will be

The correct option is 5/3.

Step-by-step Explanation:

1. Identify the given specific heat capacity of the gas at constant volume ($C_v$):

$C_v=\frac{3R}{2}$

where $R$ is the universal gas constant.

2. Use Mayer's relation, which describes the relationship between the specific heat capacity at constant pressure ($C_p$) and specific heat capacity at constant volume ($C_v$) for an ideal gas:

$C_p-C_v=R$

3. Calculate $C_p$ by substituting the value of $C_v$ into the equation:

$C_p=C_v+R$

$C_p=\frac{3R}{2}+R=\frac{5R}{2}$

4. The ratio of specific heats ($\gamma$) is defined as the ratio of $C_p$ to $C_v$:

$\gamma =\frac{C_p}{C_v}$

5. Substitute the values of $C_p$ and $C_v$ to find $\gamma$:

$\gamma =\frac{\left(\frac{5R}{2}\right)}{\left(\frac{3R}{2}\right)}=\frac{5}{3}$

Thus, the value of $\gamma$ is $\frac{5}{3}$.