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NEET PHYSICSEasy

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,P2P_1, P_2 and P3P_3 compared with those of Charles's law represented as dotted lines. Then the correct relation is:

A

P1>P3>P2P_1 > P_3 > P_2

B

P2>P1>P3P_2 > P_1 > P_3

C

P1>P2>P3P_1 > P_2 > P_3

D

P3>P2>P1P_3 > P_2 > P_1

Step-by-Step Solution

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

  1. Analyze the Graph Axes: The problem specifies 'T-V curves', which implies Temperature (TT) is plotted on the y-axis and Volume (VV) on the x-axis.
  2. Determine the Slope: Rearranging the ideal gas equation to express TT in terms of VV: T=(PnR)VT = \left(\frac{P}{nR}\right)V. This equation represents a straight line passing through the origin (y=mxy = mx) where the slope m=PnRm = \frac{P}{nR}.
  3. Relate Slope to Pressure: The slope is directly proportional to the pressure (mPm \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 P1>P2>P3P_1 > P_2 > P_3), line 1 has the highest pressure and line 3 has the lowest. Thus, P1>P2>P3P_1 > P_2 > P_3.
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