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An ideal gas is initially at temperature $T$ arid volume $V.$ Its volume is increased by $\Delta V$ due to an increase in temperature by $\Delta T,$ pressure remaining constant. The quantity $\delta=\Delta V / v \Delta T$ varies with temperature as -
Option: 1

Option: 2

Option: 3

Option: 4

Answers (1)

best_answer

From ideal gas equation, $PV=RT ---(1)$

on $P \Delta V=R \Delta t ---(2)$

Dividing equation $(2)$ by $(1),$ we get

$\begin{aligned} & \frac{\Delta U}{V}=\frac{\Delta T}{T} \\ & \therefore \frac{\Delta V}{V \Delta T}=\frac{1}{T}=\delta \end{aligned}$

$\therefore \delta \propto \frac{1}{T}$

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

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vinayak

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