The problem concerns two isobaric processes for a fixed quantity of an ideal gas, illustrated in the provided graph with temperature (\( T \)) on the x-axis and volume (\( V \)) on the y-axis. Isobaric processes are characterized by constant pressure, while temperature and volume may vary.
Lines \( P_1 \) and \( P_2 \) on the graph represent two distinct isobaric conditions, both originating from the point \( O \). The slope of each line in a \( V-T \) diagram is indicative of the \( V \)- \( T \) relationship at constant pressure. A steeper slope corresponds to a lower pressure.
The slope of \( P_1 \) is less than the slope of \( P_2 \). For an ideal gas in a \( V-T \) graph, the relationship is given by \( V = \frac{nR}{P}T \), where \( V \) is volume, \( T \) is temperature, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( P \) is the pressure.
The slope of the line is inversely proportional to the pressure \( P \); therefore, a steeper line signifies a lower pressure.
Given that \( P_2 \) has a steeper slope than \( P_1 \), it implies that the pressure \( P_2 \) is lower than \( P_1 \).
Consequently, the correct relationship is \( P_1 > P_2 \), identifying option \( P_1 > P_2 \) as the correct choice.
