Question

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

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

Answer 1

The correct option is B $C_v=\frac{R}{\gamma -1}$

we know
(i) $C_p-C_v=R$ and
(ii)$\frac{C_p}{C_v}=\gamma$
where
$C_p=$ specific heat at constant pressure
$C_v=$ specific heat at constant volume
$\gamma =$ adiabatic index

from (ii) : $C_p=\gamma C_v$
putting this in equation (i)
$\gamma C_v-C_v=R$
$C_v(\gamma -1)=R$
so $C_v=\frac{R}{\gamma -1}$