What Is the First Law of Thermodynamics (Q = ΔU + W)?

• French B
• Geography
• German A
• German A Lit
• German ab initio
• German B
• Global Politics
• History
• History (First Exam 2028)
• Mathematics Analysis and Approaches (AA)
• Mathematics Applications & Interpretation (AI)
• Philosophy
• Physics
• Psychology
• Psychology (First Exam 2027)
• Spanish A
• Spanish A Lit
• Spanish ab initio
• Spanish B
• Sports, exercise and health science (SEHS)
• Theory of Knowledge (TOK)
• World Religions

• $Q$ is the thermal energy transferred to the system.
• $\Delta U$ is the change in the system's internal energy.
• $W$ is the work done by the system on its surroundings.

Rearranging gives $\Delta U = Q - W$. Therefore, energy supplied by heating either increases internal energy or leaves the system as mechanical work.

For example, a gas receives $500\text{ J}$ of thermal energy and does $200\text{ J}$ of work while expanding:

The gas's internal energy therefore increases by $300\text{ J}$.

For an adiabatic process, $Q=0$, so $\Delta U=-W$. If the gas expands and does positive work, its internal energy decreases. For an isovolumetric process, the volume does not change, so $W=0$ and $Q=\Delta U$.

A common misconception is to treat $W$ as work done on the gas. Under the IB Physics convention, $W$ is work done by the system; using the opposite convention reverses signs.

Exam Technique

This is HL-only content from B.4 Thermodynamics. In a calculation, state the sign convention, assign signs before substitution, show the rearrangement, and give the answer in joules. For an Explain question, explicitly connect the equation to conservation of energy rather than merely quoting it.