For a gas molecule with 6 degrees of freedom, which one of the following relations between gas constant '…
For a gas molecule with 6 degrees of freedom, which one of the following relations between gas constant ' $R$ ' and molar specific heat ' $\mathrm{C}_{\mathrm{V}}$ ' is correct?
$\mathrm{R}=\frac{\mathrm{C}_{\mathrm{v}}}{3}$
$\mathrm{R}=\frac{5 \mathrm{C}_{\mathrm{v}}}{4}$
$\mathrm{R}=\frac{\mathrm{C}_{\mathrm{v}}}{2}$
$\mathrm{R}=\frac{3 \mathrm{C}_{\mathrm{v}}}{4}$
Solution
For 6 degrees if freedom, $\mathrm{C}_{\mathrm{v}}=6 \times \frac{1}{2} \mathrm{R}=3 \mathrm{R}$
$\mathrm{R}=\frac{\mathrm{C}_{\mathrm{v}}}{3}$