Question Details

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 : 

Options

A

P3 > P2 > P1

B

P1 > P3 > P2

C

P2 > P1 > P3

D

P1 > P2 > P3

Show Answer

Correct Answer :

Option D

P1 > P2 > P3

P1 > P2 > P3

Solution :

The graph shows temperature (T) on the vertical axis and volume (V) on the horizontal axis for an ideal gas at three different constant pressures P1, P2, P3. The dotted straight lines represent Charles’s law, which states that at a fixed pressure the volume of an ideal gas varies linearly with temperature.

For an ideal gas, the equation of state is

P·V=nRT

Re‑arranging for volume at a constant amount of gas (n) and a constant pressure gives

V=nRPT

Thus the T‑V relationship for a given pressure is a straight line through the origin with slope

nRP

Since the slope is inversely proportional to the pressure, a higher pressure yields a smaller slope (a flatter line), while a lower pressure yields a steeper line.

Examining the graph, the curve that lies closest to the dotted Charles’s‑law line (i.e., the flattest line) corresponds to the highest pressure because its slope is the smallest. The next curve, a bit steeper, corresponds to the next lower pressure, and the steepest curve corresponds to the lowest pressure.

From the visual ordering of the curves we therefore infer

P1>P2>P3

That is, pressure P1 is the greatest, followed by P2, and P3 is the smallest.

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