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The First Law of Thermodynamics

Simple Explanation

The first law of thermodynamics — ΔU=Q−W — is a statement of energy conservation: a system's internal energy increases with heat added to it, and decreases by however much work it does on its surroundings.

Why Do We Need It?

This single equation ties together heat, work, and internal energy — the three central quantities of thermodynamics — and underlies the analysis of every engine, refrigerator, and thermodynamic process.

Formula

The First Law of Thermodynamics

ΔU = Q − W

A statement of energy conservation for a thermodynamic system: the change in a gas's internal energy equals the heat added to it, minus the work it does on its surroundings.

ΔU: — change in internal energy, in joules (J)
Q: — heat added to the system, in joules (J) — negative if heat leaves the system
W: — work done BY the system on its surroundings, in joules (J) — negative if work is done ON the system

When to use it: Whenever relating heat added to a system, work it does, and the resulting change in its internal energy.

Worked Example

Find the change in internal energy

A gas absorbs 8000 J of heat while doing 6000 J of work on its surroundings. Find the change in its internal energy.

Why Does This Work?

Energy cannot be created or destroyed, only converted — the heat added to a gas has to go somewhere: some of it becomes work done pushing against the surroundings, and whatever is left over increases the gas's own internal energy, which is exactly what ΔU=Q−W states.

Real-Life Example

A bicycle pump heating up as it is used

Rapidly pumping a bicycle tire makes the pump noticeably warm.

Compressing the air does negative work (work is done ON the gas, so W is negative in the first law), which — with little heat escaping in that short time — increases the gas's internal energy, raising its temperature and warming the pump.

Practice

A gas releases 3000 J of heat (Q=−3000 J) while 5000 J of work is done ON it (W=−5000 J). Find the change in internal energy.

Medium

Common mistake

Mixing up the sign convention for W — "work done BY the system" is what appears as +W in ΔU=Q−W; work done ON the system must be entered as a negative W.

Quick Review

ΔU = Q−W — a statement of energy conservation.
Q positive: heat added. W positive: work done BY the system.
Ties together heat, work, and internal energy.