Question

An ideal gas is initially at temperature $T$ and volume $V$ and at constant pressure, its volume increases by $\Delta V$ due to an increase in temperature by $\Delta T$. The quantity $\mu =\Delta V/V\Delta T$ varies with temperature as:

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

According to Charle's Law: $V=KT$
$\Rightarrow \Delta V=K\Delta T$
$\Rightarrow \frac{\Delta V}{\Delta T}=K...\left(i\right)$
$\Rightarrow \mu =\frac{\Delta V}{V\Delta T}$
$\Rightarrow \mu \propto \frac{1}{V}$
According to Charle's Law: $V\propto T$
So, $\mu \propto \frac{1}{T}$
So, graph between $\mu$ and $T$ will be a rectangular hyperbola.