Question

An ideal gas is expanding such that pT$^2$ = 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

Answer: (C)

pT$^2$ = constant
$\therefore \, \, \, \bigg(\frac{nRT}{V}\bigg)T^2 =constant \, \, or \, \, \, T^3 V^{-1} = constant$
Differentiating the equation, we get
$\frac{3T^2}{V} .dT-\frac{T^3}{V^2}dV =0 \, \, \, or \, \, \, \, 3dT=\frac{T}{V}.dV \, \, \, \, \, \, \, \, \, \, \, \, $ .....(i)
From the equation, dV = $V_{\gamma}$ dT
$\gamma$ = coefficient of volume expansion of gas =$\frac{dV}{V.dT}$
From Eq.(i) $\gamma = \frac{dV}{V.dT}=\frac{3}{T}$
$\therefore $Correct answer is (c).