In the given V-T diagram, what is the relation between pressure $P_1$ and $P_2$?

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Accepted Answer

1.  **Analyze the Ideal Gas Equation:** The behavior of an ideal gas is governed by the equation $PV = nRT$ .
2.  **Analyze the V-T Graph:** The diagram plots Volume ($V$) versus Temperature ($T$). Rearranging the ideal gas equation to express $V$ as a function of $T$ (keeping Pressure $P$ constant for each line) gives $V = \left(\frac{nR}{P}\right)T$. This is the equation of a straight line $y = mx$ passing through the origin.
3.  **Slope-Pressure Relationship:** The slope of the line ($m$) is equal to $\frac{nR}{P}$. Since $n$ and $R$ are constants, the slope is inversely proportional to the pressure ($m \propto \frac{1}{P}$). This means a line with a steeper slope (higher $V$ for a given $T$) corresponds to a lower pressure.
4.  **Conclusion:** For the relation $P_2 < P_1$ to be true, the line corresponding to $P_2$ must have a larger slope (be closer to the V-axis) than the line corresponding to $P_1$. Conversely, the line with the smaller slope represents the higher pressure ($P_1$).

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