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Two isothermal curves for n moles of a perfect gas are drawn on a PV diagram. Curve 1 corresponds to pressure P1 and curve 2 corresponds to pressure P2. If curve 1 lies entirely above curve 2 at every volume value (i.e., for the same volume, the gas on curve 1 exerts greater pressure), which of the following is correct?

1. P1 > P2
2. P1 < P2
3. P1 = P2
4. Insufficient data to draw any conclusion

Correct answer: P1 > P2

Solution

For a perfect (ideal) gas, PV = nRT. An isotherm on a P-V diagram is a hyperbola P = nRT/V. If curve 1 (labeled P1) lies above curve 2 (labeled P2) at every volume, then P1 > P2 at any given volume. This directly means T1 > T2, confirming P1 > P2.

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