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)

$\frac {3} {T}$

Answer 2

Coefficient of volume expansion,
$\gamma = V^{-1} \frac{dV}{dT}$
As PT$^2$ = constant we get (T$^3$/V) as constant
Then $\frac{1}{V^2} \left( 3 T^2 V - T^3 \frac{dV}{dT} \right) = 0$
$i.e.$ $3T^2V = T^3 \frac{dV}{dT} \, i.e. \, \frac{3}{T} = \frac{1}{V} \frac{dV}{dT}$
$i.e.$ $\gamma = \frac{3}{T}$