Question

Each molecule of gas has f degrees of freedom.The ratio $\left(C_p/C_v\right)=\gamma$ for the gas is

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

Answer 1

The correct option is C 1+(2/f)

Given :Each molecule of gas has f degrees of freedom.The ratio (Cp/Cv)=γ(Cp/Cv)=γ for the gas is

Solution :

We know that $C_v=\frac{fR}{2}$

and $C_p=C_v+R$ $\Rightarrow$ $\frac{fR}{2}+R$ $\Rightarrow$ $C_p=\frac{(f+2)}{2}R$

$\gamma =\frac{C_p}{C_v}$ = $1+\frac{2}{f}$

The Correct Opt= C