Work During a Volume Change | CAIE 9702 Paper 4 Notes

Paper 4

Physics9702

Work During a Volume Change

A gas can move a piston or push the surrounding atmosphere. Energy is then transferred by work.

The formula in this lesson applies when the pressure stays constant.

Build the constant-pressure relation

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At constant pressure, the piston geometry connects force, distance and swept volume. The derivation below gives the work relation.

W_{\mathrm{by}}=p\Delta V

Symbols

Expansion

Work done by the gas is positive. Work done on the gas is negative.

Compression

Work done by the gas is negative. Work done on the gas is positive.

W_{\mathrm{on}}=-W_{\mathrm{by}}

Expansion means the system gives energy to the surroundings as work. The first-law value is therefore negative.
Compression means the surroundings give energy to the system as work. The first-law value is therefore positive.

Worked example

Expansion read from a graph

Nitrogen expands at constant pressure from 0.18 m³ to 0.32 m³. The pressure is 1.6 × 10⁵ Pa. Find the work done on the gas (9702/42/F/M/25 Q3(b)(i)).

Find the increase in volume.
$\Delta V=0.32-0.18$
$\Delta V=0.14\ \mathrm{m^3}$
The gas expands, so work done on it is negative.
$W_{\mathrm{on}}=-p\Delta V$
$W_{\mathrm{on}}=-(1.6\times10^5)(0.14)$
$W_{\mathrm{on}}=-2.2\times10^4\ \mathrm{J}$

Answer

W_{\mathrm{on}}=-2.2\times10^4\ \mathrm{J}