Question: 39. The following graph represents the T-V curves of an ideal gas (where T is the temperature and V the volume) at three pressures \mathrm{P}_{1}, \mathrm{P}_{2} and \mathrm{P}_{3} compared with those of Charles’s law represented as dotted lines. Then the correct relation is :
(1) P_{3}>P_{2}>P_{1}
(2) P_{1}>P_{3}>P_{2}
(3) P_{2}>P_{1}>P_{3}
(4) P_{1}>P_{2}>P_{3}
Answer: Option (4)
Explanation:
For an ideal gas at constant pressure, Charles’s law states that temperature is directly proportional to volume, given by T \propto V.
This relation can be written as T = \frac{P}{nR} V,
where P is the pressure, n is the number of moles,
and R is the gas constant.
Thus, in a T versus V graph,
the slope of the straight line is \frac{P}{nR}.
Therefore, the slope of the graph is directly proportional to the pressure.
A higher pressure corresponds to a steeper T–V line,
while a lower pressure corresponds to a less steep line.
From the given graph, the curve labeled P_{1} has the greatest slope,
followed by P_{2}, and then P_{3} with the least slope.
Hence, the correct order of pressures is P_{1} > P_{2} > P_{3}.