Question

A cyclic process is shown in the given $P-T$ digram of an ideal gas. Which of the following curves shows the same process in $P-V$ diagram:

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

From the given curve we can conclude that:

Pressure is constant from $\text{C to A}$, hence, in $P-V$ curve pressure is also going to be constant from $\text{C to A}$. Temperature is decreasing during this process. Therefore, on $P-V$ curve temperature will also decrease. Which will lead to decrase in the volume of the gas.

It is clear that during the process $\text{A to B}$:
$P\propto T$
As, $PV=nRT$ for ideal gas.
Hence, $V$ is constant during process $\text{A to B}$. As pressure is increasing during this process, pressure will also increase on $P-V$ curve.

Temperature is constant from $\text{B to C}$ and pressure is decreasing.
As, $PV=nRT$ for ideal gas.
Hence, during this process $\Rightarrow P\propto \frac{1}{V}$ from $\text{B to C}$. Here pressure is decreasing therefore volume will increase.

Hence, graph $\left(a\right)$ satisfies all the conditons.