Question

In an adiabatic process, $R=\frac{2}{3} C_{v} .$ The pressure of the gas will be proportional to:

• A. $T^{5 / 3}$
• B. $T^{5 / 2}$
• C. $T^{5 / 4}$
• D. $T^{5 / 6}$

Answer 1

Answer: (B)

$R=\frac{2}{3} C_{V}$
We know, $C_{p}-C_{V}=R$
or $\gamma-1=\frac{R}{C_{v}}$ or $R=C v(\gamma-1)$
Comparing $\gamma=\frac{5}{3}$
$P^{1-\gamma} T^{\gamma}=$ constant $= K$
or $P \propto T^{(\gamma / \gamma-1)}$,
Given $\gamma=\frac{5}{3}$
$\frac{\gamma}{(\gamma-1)}=\frac{5}{2}$
So, $P \propto T^{5 / 2}$