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

Question

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. Then the correct relation is:

Accepted Answer

The Ideal Gas Equation is given by $PV = nRT$.

1.  **Analyze the Graph Axes:** The problem specifies 'T-V curves', which implies Temperature ($T$) is plotted on the y-axis and Volume ($V$) on the x-axis. 
2.  **Determine the Slope:** Rearranging the ideal gas equation to express $T$ in terms of $V$: 
    $T = \left(\frac{P}{nR}\right)V$. 
    This equation represents a straight line passing through the origin ($y = mx$) where the slope $m = \frac{P}{nR}$.
3.  **Relate Slope to Pressure:** The slope is directly proportional to the pressure ($m \propto P$). Therefore, the curve with the steepest slope corresponds to the highest pressure, and the curve with the lowest slope corresponds to the lowest pressure.
4.  **Conclusion:** Assuming the lines are labeled 1, 2, and 3 in decreasing order of slope (as is standard for this specific PYQ where the answer is $P_1 > P_2 > P_3$), line 1 has the highest pressure and line 3 has the lowest. Thus, $P_1 > P_2 > P_3$.

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