Question

An ideal monoatomic gas is expanding such that $P{T}^2=constant$. The molar specific heat of the gas is :

• A. $\frac{11R}{2}$
• B. $\frac{7R}{2}$
• C. $\frac{5R}{2}$
• D. $\frac{9R}{2}$

Answer 1

The correct option is D $\frac{9R}{2}$

The given relation is $P{T}^2=constant$
Substituting $T=\frac{PV}{R}$ in the above relation,

we get $P\times (\frac{PV}{R}{)}^2=constant$

$⟹P{V}^{2/3}=constant$

Comparing this with $P{V}^{\eta }=constant$
Hence, we get polytropic exponent $\eta =\frac{2}{3}$

Also, for monoatomic gas $\gamma =\frac{5}{3}$
$\therefore$ Molar specific heat $C=\frac{R}{\gamma -1}-\frac{R}{\eta -1}$ $=\frac{R}{\frac{5}{3}-1}-\frac{R}{\frac{2}{3}-1}$

$⟹C=\frac{3}{2}R+3R=\frac{9}{2}R$