JEE Physics 2023 Question with Solution

Given: An isothermal change on a $P$-$V$ graph for three temperatures satisfying $T_3 > T_2 > T_1$.

Find: Which graph correctly represents the pressure-volume relation.

For an isothermal process, the relation is

So, the $P$-$V$ curve is a rectangular hyperbola.

Also,

For the same amount of gas, a higher temperature means a larger value of $PV$. Therefore, the isotherm for higher temperature lies farther from the origin on the $P$-$V$ graph.

Since $T_3 > T_2 > T_1$, the outermost curve must correspond to $T_3$, the middle curve to $T_2$, and the innermost curve to $T_1$.

Therefore, the correct graph is Option D.

Given: Three isothermal curves and the condition $T_3 > T_2 > T_1$.

Find: The correct ordering of curves on the $P$-$V$ diagram.

The solution hint uses a horizontal dotted line, which represents an isobaric line, meaning pressure is the same for all three intersections.

At the same pressure, from the ideal gas law,

If $P$ is fixed, then

Hence, larger volume means higher temperature.

Along the dotted horizontal line, the curve intersecting at the largest volume corresponds to $T_3$, then $T_2$, and then $T_1$. So the correct arrangement is the one where the hyperbolas move farther from the origin as temperature increases.

Therefore, the correct option is D.