Question

An ideal gas is expanding such that $PT=$ constant. The coefficient of volume expansion of the gas is :

• A. $\frac{1}{T}$
• B. $\frac{2}{T}$
• C. $\frac{3}{T}$
• D. $\frac{4}{T}$

Answer 1

The correct option is B $\frac{2}{T}$

Given, $PT$ = constant
Using the ideal gas equation $PV=nRT$, we can say that
$\frac{nRT}{V}\times T=$ constant
$\Rightarrow \frac{T^2}{V}=k\left(\text{say}\right)$
Differentiating both sides w.r.t $T$, we get
$\frac{2T}{V}-\frac{T^2}{V^2}\frac{dV}{dT}=0$
Coefficient of volume expansion is given by
$\alpha =\frac{dV}{VdT}$
$\therefore \alpha =\frac{dV}{VdT}=\frac{2TV}{V{T}^2}=\frac{2}{T}$
Thus, option (b) is the correct answer.