Question

For a gas having molar mass $M$, specific heat at constant pressure is given by:

• A. $\frac{\gamma R}{M(\gamma -1)}$
• B. $\frac{\gamma }{RM}$
• C. $\frac{M}{R(\gamma -1)}$
• D. $\frac{\gamma RM}{(\gamma +1)}$

Answer 1

The correct option is A $\frac{\gamma R}{M(\gamma -1)}$

we know
$C_p-C_v=Rand\frac{C_p}{C_v}=\gamma$.......(i)

$C_p=$ heat capacity at constant pressure
$C_v=$ heat capacity at constant volume
$\gamma =$ adiabatic index

To get the specific heat capacity, (heat capacity per unit mass) divide by molar mass
$C_p-C_v=\frac{R}{M}$
using equation (i)
$\therefore C_p-\frac{C_p}{\gamma }=\frac{R}{M}{C}_p\left(\frac{\gamma -1}{\gamma }\right)=\frac{R}{M}or{C}_p=\frac{R\gamma }{M(\gamma -1)}$