The first law of thermodynamics

Physics A2 · Thermodynamics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

Test this topic free All Physics A2 topics

The idea

There are two ways to change the internal energy of a system: transfer energy to it by heating, or do work on it. The first law of thermodynamics is the conservation of energy written for this: the increase in internal energy equals the heating of the system plus the work done on the system.

A gas does work when its volume changes. If it expands, it pushes its surroundings back, so work is done by the gas and the work done on the gas is negative. If it is compressed, work is done on the gas and W is positive.

Every term has a sign. Decide the sign of q and of W before you put numbers in.

Rules to remember

Work done at constant pressure = pressure × change in volume (W = pΔV), with p in Pa and V in m³
First law: increase in internal energy = energy supplied by heating + work done on the system (ΔU = q + W)
q is positive when energy enters by heating and negative when it leaves
W is positive for a compression (work done on the gas) and negative for an expansion (work done by the gas)
Work done on the gas = −(work done by the gas)
On a p–V graph, the area under the line is the work done
Ideal gas at constant temperature: ΔU = 0, so q = −W. No heating (insulated): q = 0, so ΔU = W. 1 cm³ = 10⁻⁶ m³

Common mistake

The most common mistake is a sign error: adding the work when the gas expands. In ΔU = q + W, W is the work done on the gas, so an expanding gas has a negative W.

Worked example

A gas is compressed at a constant pressure of 1.5 × 10⁵ Pa from 6.0 × 10⁻³ m³ to 2.0 × 10⁻³ m³. During the compression 800 J of energy leaves the gas by heating. What is the change in its internal energy?

Decrease in volume = 6.0 × 10⁻³ − 2.0 × 10⁻³ = 4.0 × 10⁻³ m³.
Work done on the gas: W = pΔV = 1.5 × 10⁵ × 4.0 × 10⁻³ = +600 J (compression, so positive).
Energy leaves by heating, so q = −800 J.
ΔU = q + W = −800 + 600 = −200 J.

Answer: The internal energy decreases by 200 J.

Ask about this

Type what you are stuck on. The helper finds the explanation, worked examples and the notes to read, free and instant.

Read the full notes

Full-course notes

Keep going

← Internal energy Simple harmonic oscillations →Take a Physics A2 test