Question

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

• A. $(1+\frac{2}{n})$
• B. $(1+\frac{n}{2})$
• C. $(1+\frac{1}{n})$
• D. $(1+\frac{n}{3})$

Answer 1

The correct option is A $(1+\frac{2}{n})$

The internal energy for 1 mole of gas is given as $U=\frac{n}{2}RdT=C_{v}dT$

where n is degrees of freedom

$C_p-C_v=R$

$Cp=(1+\frac{n}{2})R$

and $\frac{C_p}{C_v}=\gamma =\frac{(1+\frac{n}{2})R}{\frac{n}{2}}=1+\frac{2}{n}$