Question

Choose the correct option related to the specific heat at constant volume $C_v$

• A. $C_v=\frac{R}{\gamma -1}$
• B. $C_v=\frac{1}{2}fR$
• C. $C_v=\frac{C_p}{\gamma }$
• D. All of these

Answer 1

The correct option is D All of these

We know that: $C_p-C_v=R$
Dividing by $C_v$
$\frac{C_p}{C_v}-1=\frac{R}{C_v}$
Also we know, $\frac{C_p}{C_v}=\gamma$
$\gamma -1=\frac{R}{C_v}$
$C_v=\frac{R}{\gamma -1}$
$U=\frac{f}{2}RT$
$C_v=\frac{dU}{dT}=\frac{f}{2}R$