2024 Kinetic TheoryCharles's Law (Isobaric T-V Graphs) Medium Question 5 of 34 in Kinetic Theory

The following graph represents the T-V curves of an ideal gas (where T is the temperature and V the volume)…

The following graph represents the T-V curves of an ideal gas (where T is the temperature and V the volume) at three pressures $P_1$, $P_2$ and $P_3$ compared with those of Charles's law represented as dotted lines.
A $P_2 > P_1 > P_3$
B $P_1 > P_2 > P_3$
C $P_3 > P_2 > P_1$
D $P_1 > P_3 > P_2$

The answer is B.

Solution

From the ideal gas equation $PV = nRT$: $T = \left(\frac{P}{nR}\right)V$, i.e. $T \propto V$ with slope $\frac{P}{nR}$ So a steeper T-V line corresponds to a higher pressure. From the graph, the $P_1$ curve is steepest and $P_3$ is least steep. So $P_1 > P_2 > P_3$.

Concept Comparing isobars on a T-V graph

Kinetic Theory in past papers

34 questions from this chapter have appeared across 19 exam years.