Rankers Physics
Topic: Thermal Physics
Subtopic: Thermodynamics

Pressure versus temperature graph of an ideal gas of equal number of moles (μ) of different volumes are plotted as shown in figure. Choose the correct alternative : Image related to
V1 = V2, V3 = V4 and V2 > V3
V1 = V2, V3 = V4 and V2 < V3
V1 = V2 = V3 = V4
V4 > V3 > V2 > V1

Solution:

For an ideal gas, at constant volume, the pressure \( P \) is directly proportional to the temperature \( T \) (Gay-Lussac's Law):

\[
P \propto T
\]

In the graph, each line represents a pressure-temperature relationship at different volumes. A steeper slope indicates a smaller volume (since \( P = \frac{nRT}{V} \) and a higher \( V \) gives a less steep line).

From the figure:
1. Lines \( 1 \) and \( 2 \) have the same slope, indicating \( V_1 = V_2 \).
2. Lines \( 3 \) and \( 4 \) also have the same slope, indicating \( V_3 = V_4 \).
3. The slope of lines \( 3 \) and \( 4 \) is steeper than that of lines \( 1 \) and \( 2 \), meaning \( V_2 > V_3 \).

Thus, the correct answer is \( V_1 = V_2 \), \( V_3 = V_4 \), and \( V_2 > V_3 \).

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