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The following graph represents the T-V curves of an ideal gas (where T is the temperature and V the volume) at three pressures P₁, P₂ and P₃ compared with those of Charles's law represented as dotted lines. Then the correct relation is:
Draw a vertical line at constant volume V: Higher T means higher pressure (P ∝ T at constant V) -> Curve P₁ is on top -> P₁ > P₂ > P₃!
For an ideal gas, the equation of state is PV = nRT. Expressing temperature T as a function of volume V:
The graph plots T on the vertical axis and V on the horizontal axis. For an isobaric line representing Charles’s law, the slope is:
Because n and R are constants, the slope of the T-V line is directly proportional to pressure P. A steeper line corresponds to a higher pressure:
From the given graph, curve P₁ is the steepest (highest slope), curve P₂ has intermediate slope, and curve P₃ has the lowest slope (gentlest inclination):
Diagnose every choice: Know exactly why the right option works and why distractors fail.
Places P₂ as largest, which has an intermediate slope.
Exact physical ranking: steeper T-V curve indicates greater pressure.
Completely inverts the pressure hierarchy.
Jumbled ordering of P₂ and P₃.
Most textbook problems plot V on the y-axis and T on the x-axis (where slope = nR/P, so higher slope means LOWER pressure). In this question, axes are reversed: T is on the y-axis!
"On a T versus V plot, the slope of an isobar is P/nR; higher slope directly indicates higher pressure."
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