Question

An ideal gas is initially at a temperature $T$ and volume $V$. Its volume is increased by $\Delta V$ due to an increase in temperature $\Delta T$, pressure remaining constant. The quantity $\delta =\Delta V/\left(V\Delta T\right)$ varies with temperature as

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

From ideal gas equation
$\begin{array}{c}PV=nRT\left(1\right)\\ P\Delta V=nR\Delta T\left(2\right)\end{array}$

Dividing equation $\left(2\right)$ by equation $\left(1\right)$, we get

$\frac{\Delta V}{V}=\frac{\Delta T}{T}\Rightarrow \frac{\Delta V}{V\Delta T}=\frac{1}{T}=\delta$

$\delta =\frac{1}{T}$

So the graph between $\delta$ and $T$ will be a rectangular hyperbola.