Choose the correct option for graphical representation of Boyle’s law, which shows a graph of pressure vs. volume of a gas at different temperatures :

Boyle’s law states that, for a fixed amount of gas at a constant temperature, the pressure $P$ of the gas is inversely proportional to its volume $V$:

$P · V = k$ where $k$ is a constant for a given temperature.

When the temperature is changed while keeping the amount of gas the same, the constant $k$ also changes. A higher temperature gives a larger $k$, which means for any particular volume the pressure will be higher.

Therefore, on a pressure‑versus‑volume graph that includes several isotherms (different temperatures), the correct graphical representation must satisfy two conditions:

• Each individual curve must be a hyperbola (decreasing curve) because pressure falls as volume rises at a fixed temperature.
• Curves corresponding to higher temperatures must lie above those for lower temperatures at the same volume, reflecting the larger $k$ values.

The image selected as the correct answer (the second option) shows exactly these features:

• All four curves are smooth, continuously‑decreasing hyperbolas.
• The curve labeled with the highest temperature is the topmost one, and the curve for the lowest temperature is the bottommost one.
• The axes are correctly labeled “Pressure (P)” on the vertical axis and “Volume (V)” on the horizontal axis, matching the quantities asked for in the question.

By contrast, the other three images either display straight‑line relationships, intersecting curves that do not preserve the ordering by temperature, or axes that are mislabeled. Those characteristics violate Boyle’s law and therefore cannot be the correct representation.

Consequently, the graph of pressure versus volume that correctly illustrates Boyle’s law at different temperatures is the second image shown in the options.