Work from a Pressure-Volume Graph | CAIE 9702 Paper 4 Notes

Chapters

Paper 4

Physics9702

Work from a Pressure-Volume Graph

A pressure-volume graph can show volume work as an area.

This lesson uses a horizontal path, so the gas pressure is constant.

Area under a constant-pressure path

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At constant pressure, the work done by the gas is the area under the p-V path. Motion to the right is expansion.

The area under a pressure-volume path represents work done by the gas.
At constant pressure, the path is horizontal and the area is a rectangle. Its height is pressure and its width is the volume change.

Worked example

A very small expansion

A heated aluminium block expands from 3.612 × 10⁻³ m³ to 3.722 × 10⁻³ m³ at pressure 1.01 × 10⁵ Pa. Find the magnitude of the work done and compare it with an internal-energy increase of 4.38 MJ (9702/42/M/J/25 Q3(b)(iii)-Q3(c)).

$3.722-3.612=0.110$
$\Delta V=0.110\times10^{-3}$
$\Delta V=1.10\times10^{-4}\ \mathrm{m^3}$
$|W|=p\Delta V$
$p=1.01\times10^5\ \mathrm{Pa}$
$\Delta V=1.10\times10^{-4}\ \mathrm{m^3}$
$|W|=11.1\ \mathrm{J}$
The work is tiny beside 4.38 × 10⁶ J, so it is negligible in the energy calculation.

Answer

|W|=11.1\ \mathrm{J}

Comparison: 11.1 J is negligible beside 4.38 MJ.