The two lines that go at the top of every problem
- 1
Define the system and the boundary
What's inside, what's outside, and does anything cross? Gas in the cylinder, or gas plus cylinder? This determines whether work terms appear at all, and getting it wrong invalidates everything after.
- 2
State the sign convention explicitly
Write it down: heat into the system is positive, work done by the system is positive — or whatever your course uses. Textbooks differ, and half of all sign errors are silently switching mid-problem.
- 3
Classify the system
Open, closed or isolated. Which terms survive? An isolated system kills most of the equation immediately.
- 4
Classify the process
Isothermal, adiabatic, isobaric, isochoric, reversible? Each sets a term to zero or fixes a relationship, and identifying it is usually the whole difficulty of the question.
- 5
Only then write the first law
With the terms you've just established. Most students start here and spend the rest of the question fixing the consequences.
This takes ninety seconds and it's the single highest-return habit in the subject. Make it a physical routine so it survives exam pressure.
Understand entropy three ways
Entropy is where the subject loses people, largely because it's usually presented in only one of its three characterisations and students are left with a definition they can't reason from.
| Framing | Statement | Use it for |
|---|---|---|
| Macroscopic | dS = dQ_rev / T | Calculation. This is the one you compute with. |
| Statistical | S = k ln W — a count of microstates | Understanding why entropy increases at all. |
| Practical | A measure of energy unavailable to do work | Engine efficiency and why perpetual motion fails. |
You need all three, and the exam usually tests the one you didn't study. If you can only calculate, an explanation question defeats you; if you only have the intuition, the calculation does. Explain each out loud in ninety seconds as a check — the Feynman stall finds the missing one fast.
Which potential, and why there are four
Internal energy, enthalpy, Helmholtz and Gibbs free energy look like four arbitrary quantities to memorise. They're the same information organised for four different constraint situations, and knowing which constraint each suits is what the exam tests.
- Constant volume and entropy → internal energy. Rare in practice, which is why the others exist.
- Constant pressure → enthalpy. Almost all chemistry, because reactions happen in open vessels at atmospheric pressure.
- Constant temperature and volume → Helmholtz. Common in physics and statistical mechanics.
- Constant temperature and pressure → Gibbs. Almost all biochemistry and most spontaneity questions.
Learn the constraint-to-potential mapping first and the Legendre transforms second. Students who memorise the definitions without the mapping can write all four and can't choose one, which is precisely what a problem asks for.
Practise recognition, not just calculation
Textbook problem sets are grouped by chapter, so you always know it's an adiabatic problem because you're in the adiabatic chapter. The exam gives you a scenario and expects you to identify the process — and misidentifying it makes the whole answer wrong regardless of how well you execute.
- Drill classification separately. Take twenty problem statements and, for each, write only the system, the process type and which terms vanish. Fifteen seconds each, no solving. This is the highest-yield five minutes in the subject.
- Mix chapters deliberately. Interleaved sets are the only ones that train identification.
- Learn the verbal cues. "Insulated", "slowly", "rigid container", "in contact with a reservoir" each specify a process, and recognising them is a vocabulary skill worth drilling directly.
- Sanity-check every answer. Did entropy decrease in an isolated system? Is your efficiency above Carnot? These checks catch errors in seconds and are free marks.
Statistical mechanics, if your course includes it
The transition from classical to statistical thermodynamics is where many courses lose students, because it changes what the subject is about — from measurable quantities to counting arguments over microstates.
The bridge worth over-learning is the partition function: once you have it, every thermodynamic quantity follows by differentiation. Students who treat the partition function as one topic among many end up memorising a dozen results that are all consequences of one. Derive the standard results from it repeatedly rather than memorising them — how to memorise formulas covers when derivation beats recall.
Chemistry versus physics versus engineering courses
The same subject is taught with genuinely different emphases and it's worth knowing which you're in, because the revision priorities differ sharply. Chemical thermodynamics concentrates on Gibbs energy, equilibrium and reaction spontaneity. Physical thermodynamics goes deeper into statistical foundations and idealised cycles. Engineering thermodynamics is dominated by real cycles, steam tables and efficiency calculations with property data.
Check which one your past papers reflect before allocating time — and if you're in an engineering course, get fluent with the property tables early, because table lookup speed is a real component of exam performance and is trained only by doing it repeatedly. How to study engineering and how to study physics cover the wider habits.