Question

An ideal gas is expanding such that $P T=$ 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: (B)

$P T=$ Constant
or $\frac{T^{2}}{V}=$ Constant
$[P V=n R T] $
$\Rightarrow T_{2}=K V \ldots$ (i)
Differentiating w.r.t. $T$, we get
$\frac{2 T}{V}-\frac{K}{V} \frac{d V}{d T} $
$\Rightarrow \frac{2 T}{V K}=\frac{d V}{V d T} $
$\therefore \frac{d V}{V d T}=\frac{2 T V}{V T^{2}}=\frac{2}{T}$