Question

The ratio of the specific heats $\frac{C_p}{C_v}=\gamma$ in terms of degrees of freedom (n) is given by :

• A. (1+n/2)
• B. (1+1/n)
• C. (1+n/3)
• D. (1+2/n)

Answer 1

The correct option is D

(1+2/n)

For a monoatomic gas

$C_v=\frac{3}{2}R{C}_p=\frac{5}{2}R\gamma =\frac{C_p}{C_v}=\frac{5}{3}$

For a diatomic gas

$C_v=\frac{5}{2}R{C}_p=\frac{7}{2}R\gamma =\frac{C_p}{C_v}=\frac{7}{5}$

For a triatomic gas

$C_v=3R{C}_p=4R\gamma =\frac{C_p}{C_v}=\frac{4}{3}$

This fits into the pattern $(1+\frac{2}{n})$ , where n is the number of the degrees of freedom.