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
$\therefore \left(\frac{nRT}{V}\right)T^2=constantor{T}^3{V}^{-1}=constant$
Differentiating the equation, we get
$\frac{3T^2}{V}.dT-\frac{T^3}{V^2}dV=0or3dT=\frac{T}{V}.dV$ .....(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).