Which of the following graphs represent the behavior of an ideal gas? Symbols have their usual meaning.

Solution

Physics sir · 3 steps

Read the axes first: PV = nRT says PV grows in step with T, so look for a rising straight line.

1. Use the gas law. For a fixed amount of ideal gas, n and R are constants. So the ideal gas equation ties the product PV directly to the absolute temperature.

   PV = nRT ⇒ PV ∝ T

2. Shape of the graph. A direct proportion plotted as PV against T is a straight line with a positive slope of nR. Extended back, it would pass through the origin. If T doubles, PV doubles.

   Option	What the graph shows	Matches PV ∝ T?
   (a)	Straight line, PV falls as T rises	No, wrong direction
   (b)	Horizontal line, PV constant	No, ignores T
   (c)	Straight line, PV rises with T	Yes
   (d)	Curve, PV falls as T rises	No, wrong direction and not linear

3. So. Only graph (c) shows PV increasing linearly with T, so it represents an ideal gas. The answer is (c).

The idea to keep. Before matching a gas graph, check what is on each axis. Then write PV = nRT in the form of those two quantities and read off the shape: here PV against T must be a rising straight line.

Answer from the NTA final answer key. Solution by PrepWiser.