Question

For polytropic process $P{V}^n=constant,C_m$ (molar heat capacity) of an ideal gas is given by

• A. $C_{v,m}-\frac{R}{(n-1)}$
• B. $C_{v,m}+\frac{R}{(1-n)}$
• C. $C_{v,m}+R$
• D. $C_{v,m}+\frac{R}{(1-n)}$

Answer 1

The correct option is B

$C_{v,m}+\frac{R}{(1-n)}$

$du=dq+dw$

$n{c}_{v,m},dT=n{c}_m.dT-p.dv$

$L_m=c_{v,m}+\frac{p.dV}{n.dT}$..........(1)

$p{V}^n=K$ and $pV=nRT$

$K(1-n)V^{-n}{V}^{-n}dV=nRdT$

$\frac{dV}{dT}=\frac{nR}{K(1-n)V^{-n}}$...........(2)

From (1) & (2)

$c_m=C_{v,m}+\frac{R}{(1-n)}$