Physics

Physics

Problem

A gas expands from 0.010 m30.010\,\text{m}^3 to 0.040 m30.040\,\text{m}^3 along two alternative paths. Path A: The pressure remains constant at 2.0×105 Pa2.0\times10^{5}\,\text{Pa}. Path B: The pressure decreases linearly with volume from 6.0×105 Pa6.0\times10^{5}\,\text{Pa} at 0.010 m30.010\,\text{m}^3 to 2.0×105 Pa2.0\times10^{5}\,\text{Pa} at 0.040 m30.040\,\text{m}^3. Which statement correctly compares the work WAW_A done BY the gas along Path A with the work WBW_B done along Path B? a) WBW_B is three times WAW_A. b) WBW_B equals WAW_A. c) WBW_B is twice WAW_A.},{ d) WAW_A exceeds WBW_B.
Intuitive explanation

Work done by a gas during expansion is the area under the curve on a PP–VV diagram. Path A is a horizontal line (constant pressure), so its work is simply P×ΔVP \times \Delta V. Path B is a slanted line starting higher but ending at the same pressure, so it encloses a larger area under the curve. The key insight is that even though both paths start and end at the same volume and final pressure, the path that maintains higher pressure for longer does more work—so you're comparing a rectangle to a trapezoid with the same base but greater height on average.

Intuitive explanation

Work done by a gas during expansion is the area under the curve on a PP–VV diagram. Path A is a horizontal line (constant pressure), so its work is simply P×ΔVP \times \Delta V. Path B is a slanted line starting higher but ending at the same pressure, so it encloses a larger area under the curve. The key insight is that even though both paths start and end at the same volume and final pressure, the path that maintains higher pressure for longer does more work—so you're comparing a rectangle to a trapezoid with the same base but greater height on average.

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