Thermodynamics · Quick Reference

First Law of Thermodynamics Cheat Sheet

Thermodynamics · Lesson 7/10

In one line: the first law of thermodynamics is really just energy conservation applied to heat and work — energy can change form or move around, but it can never be created or destroyed.

Key Ideas

1The First Law Statement. The change in a system's internal energy equals the heat added to the system minus the work done BY the system: delta_U = Q - W.

2Internal Energy (U). The total kinetic and potential energy of all the particles within a system -- roughly, the system's total 'thermal content'.

3Sign Conventions. Q is positive when heat is added to the system; W is positive when the system does work on its surroundings (like an expanding gas pushing a piston).

4Special Cases. Isothermal (constant temperature, so delta_U=0, meaning Q=W). Adiabatic (no heat exchange, so Q=0, meaning delta_U=-W). Isochoric (constant volume, so W=0, meaning delta_U=Q).

5Why the First Law Matters. It guarantees that no process -- no engine, no chemical reaction, no biological system -- can create energy from nothing or destroy it; energy is always conserved, just converted.

Worked Examples

A gas absorbs 500 J of heat and does 200 J of work on its surroundings. Find the change in internal energy.

300 J

A gas has 300 J of work done ON it (compression) with no heat exchange (adiabatic). Find the change in internal energy.

300 J (internal energy increases, since compression adds energy without heat loss)

In an isothermal process, why does Q equal W exactly?

Because delta_U=0 at constant temperature, the first law reduces to Q=W

Formulas

delta_U = Q - W

Practice Yourself

A gas absorbs 800 J of heat and does 300 J of work. Find delta_U.

500 J

A gas releases 200 J of heat and has 100 J of work done on it. Find delta_U. (Q=-200, W=-100)

delta_U=-200-(-100)=-100 J

What does 'adiabatic' mean?

No heat exchange occurs (Q=0)