Question

An ideal gas undergoing cyclic process $ABCA$ is shown in the $P-T$ diagram. Which of the following curves correctly represents the process on a $V-T$ diagram?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Process $AB$ on $P-T$ curve:
$\frac{P}{T}=$ constant
$\Rightarrow$ Volume constant (as, $PV=nRT$)
$\Rightarrow$ On, $V-T$ curve, it will be a horizontal line left to right.

Process $BC$ on $P-T$ curve:
Temperature constant it is isothermal process.
$\Rightarrow PV=\text{constant}\Rightarrow P\propto \frac{1}{V}$
$\Rightarrow$ On $V-T$ curve it will be a vertical line with increasing volume.

Process $CA$ on $P-T$ curve:
Pressure constant it is isobaric process with decreasing temperature
$\Rightarrow T\propto V$
(From ideal gas equation $PV=nRT$.
When $P$ = constant)
$\Rightarrow$ On $V-T$ curve it will be inclined downwards.
Only option (b), matches all the conclusions.

$\begin{array}{c}\text{Why this question}?\\ \text{One should know how to interpret and}\\ \text{and analyze property diagram.}\end{array}$