Internal Energy and Work
Simple Explanation
A gas's internal energy is the total kinetic (and, for real gases, potential) energy of all its particles. When a gas expands at constant pressure, it does work on its surroundings, W=PΔV — exactly the area under a horizontal line on a pressure-volume (P-V) graph.
Why Do We Need It?
This is the essential first step to understanding thermodynamics quantitatively — every heat engine, refrigerator, and thermodynamic cycle is built from processes where a gas does (or has done to it) exactly this kind of work.
See It
A pressure-volume graph with a horizontal line at pressure P from volume V1 to V2, with the rectangular region beneath it shaded to represent the work done
Formula
Work Done by a Gas at Constant Pressure
W = PΔV
When a gas expands or is compressed at constant pressure, the work it does (or has done on it) equals the pressure times the change in its volume — exactly the area under a horizontal line on a pressure-volume graph.
- W
- — work done by the gas, in joules (J)
- P
- — the (constant) pressure of the gas, in pascals (Pa)
- ΔV
- — change in volume (final minus initial), in cubic metres (m³)
When to use it: Whenever the work done by (or on) a gas expanding or compressing at constant pressure needs to be found.
Worked Example
Find the work done by an expanding gas
A gas expands at a constant pressure of 200000 Pa from a volume of 0.02 m³ to 0.05 m³. Find the work it does.
Why Does This Work?
Work is force times distance; the force a gas exerts on a piston is pressure times the piston's area (F=PA), and the distance the piston moves times its area is exactly the change in volume — so W=F×distance becomes W=PA×(distance)=PΔV.
Real-Life Example
A piston pushed outward in a car engine
Inside a car engine cylinder, hot expanding combustion gases push a piston outward, doing work that ultimately turns the wheels.
That work done by the expanding gas on the piston is exactly W=PΔV, computed the same way for every stroke of every cylinder in the engine.
Practice
A gas is compressed at constant pressure 150000 Pa from 0.04 m³ to 0.01 m³. Find the work done BY the gas (it will be negative, since the gas is compressed, not expanded).
MediumCommon mistake
Forgetting the sign convention — work done BY the gas is positive during expansion (ΔV>0) and negative during compression (ΔV<0), since the gas is having work done ON it instead.
Quick Review
- W = PΔV, valid at constant pressure.
- Equals the area under a horizontal line on a P-V graph.
- Positive for expansion, negative for compression.