Question

The P-V relation for a monatomic ideal gas undergoing an adiabatic change is :

• A. $P{V}^{5/3}=constant$
• B. $P{V}^2=constant$
• C. $P{V}^{2/3}=constant$
• D. $P{V}^{7/3}=constant$

Answer 1

Answer: (A)

$P{V}^{5/3}=constant$

We know, mono atomic gas has 3 degree of freedom

$\frac{C_p}{C_v}=\gamma$

$\gamma =\frac{f+2}{f}$

$\gamma =\frac{3+2}{3}$

$\gamma =\frac{5}{3}$

Mono atomic ideal gas in adiabatic change is,

$P{V}^{\gamma }=constant$

So, putting the value of $\gamma$ we get,

$P{V}^{5/3}=constant$