IB Physics: Internal Energy & the First Law of Thermodynamics

You need three things: internal energy is the sum of random kinetic and potential energies of a substance's particles; the first law states ΔU = Q + W (energy added by heating plus work done on the gas); and you must apply this to the four ideal-gas processes — isovolumetric, isobaric, isothermal, adiabatic — reading pressure-volume graphs correctly.

Temperature measures the average kinetic energy per particle; internal energy is the total energy (kinetic plus potential) of every particle in the whole system. Two blocks of the same substance at identical temperature but different mass have the same average particle energy but very different internal energy — mass matters for one, not the other.

It's energy conservation applied to gases: whatever internal energy a system gains (ΔU) must come from heat added to it (Q) plus work done on it (W) by its surroundings. If a gas does work on its surroundings instead, that energy leaves the system, so W in the equation becomes negative in the IB's convention.

The IB Physics guide uses ΔU = Q + W, where Q is positive when heat is added to the system, and W is positive when work is done ON the gas (compression). If the gas expands and does work on its surroundings, W is negative — this is the single most common source of dropped marks on this topic.

Work done equals the area under the pressure-volume curve. For expansion, the gas does work on the surroundings (energy leaves the system); for compression, work is done on the gas (energy enters). At constant pressure, work simplifies to W = pΔV, which HL students must apply directly.

Isovolumetric: no work done (ΔV = 0), so ΔU = Q. Isobaric: pressure constant, W = −pΔV (expansion), heat and work both contribute to ΔU. Isothermal: temperature constant, so ΔU = 0, meaning Q = −W exactly. Adiabatic: no heat exchange (Q = 0), so ΔU = W entirely.

Internal energy for an ideal gas depends only on temperature (specifically the average kinetic energy of particles), and an isothermal process is defined as one where temperature stays constant throughout. No temperature change means no change in average particle kinetic energy, so ΔU must equal zero — even though heat and work are both non-zero.

An adiabatic process is one where the system is thermally insulated or the change happens too fast for heat to flow — a rapidly compressed gas in a bicycle pump, for example. Since Q = 0, all the internal energy change comes from work: ΔU = W. This is why rapid compression heats a gas noticeably.

The top three: mixing up whether work done is positive or negative for expansion versus compression; forgetting that isothermal means ΔU = 0 (not Q = 0); and using ΔU = Q − W (the physics convention) instead of the IB's ΔU = Q + W, which flips your final sign entirely.

SL students need the qualitative first law (ΔU = Q + W) and to describe the four processes conceptually. HL students must additionally calculate work done from p-V graphs, apply the law quantitatively across multi-step processes, and connect it to entropy and the second law — none of which SL sees.

Work backwards from past-paper p-V graph questions rather than re-reading notes. Practise identifying the process type first (look at what's held constant), fill in the sign table from memory, then substitute. Most marks lost here are process-identification errors, not calculation errors.

Internal energy is a property the system has (a state function) — it depends only on the current state, not how it got there. Heat and work are not properties of the system; they're methods of energy transfer, and both depend on the path taken between two states, which is why the same ΔU can come from different combinations of Q and W.

HL adds quantitative p-V graph calculations and multi-step process questions that SL doesn't see, making it noticeably harder — but it's a small, well-defined topic, so it's genuinely learnable with focused practice rather than broad revision. Thermal Energy Transfers questions appear reliably across Paper 1 and Paper 2 each session.