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IPhO Thermodynamics & Statistical Physics Problem Set (Official Problems + Hints)

Curated IPhO thermo/stat problems grouped by technique (first/second law, distributions, transport), with outlines and common traps.

  • International Physics Olympiad preparation

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Thermo/stat marks are often won by disciplined bookkeeping: define the system, state constraints, and use the second law as an inequality tool.

Before you start

If you have not done the hub path yet, start with the IPhO Thermodynamics & Statistical Physics Hub.

Source PDFs

Archive mirror index: https://phoxiv.org/contests/ipho

Official documentations page: https://www.ipho-new.org/documentations/

Fading-hint route (recommended order)

  1. Read the framework once: IPhO Problem-Solving Framework

  2. Do the hub Entry and Core lessons first (then return here):

  3. Start with sections A and B below (starter problems).
  4. Finish the hub lessons, then do sections C and D (core).
  5. Do sections E and F (stretch) after you are comfortable.
Show the full hub lesson path (Thermo/Stat | IPhO Prep)
  1. First Law Problem Patterns
  2. Entropy & Second Law Problem Patterns
  3. Kinetic Theory & Equipartition
  4. Boltzmann Distribution Intuition
  5. Transport: Heat Conduction & Diffusion Scaling
  6. Thermodynamic Potentials & Maxwell Relations

A. Energy Balance and First-Law Bookkeeping

  • IPhO 2024 T3 — “Survival in the mountains” (PDF)
Outline pattern: first law without sign confusion
  • define the system and write the sign convention once (Q in? W by system?) - list energy transfers and which are zero due to constraints - write one check: if you reverse the process, the sign should flip

B. Entropy, Second-Law Constraints, and Bounds

  • IPhO 2024 T1 — “Greenhouse Effect” (PDF)
Outline pattern: second law as a bounding tool
  • compute Δ S via a reversible surrogate path
  • write Δ Sᵤₙᵢᵥ ≥ 0 and interpret it as a feasibility/bound condition
  • keep one “order-of-magnitude” energy balance line for sanity

C. Statistical Thinking and “Which Term Dominates?”

  • IPhO 2018 T3 — “Physics of Live Systems” (PDF)
  • IPhO 2023 T1 — “Soil Colloids” (PDF)
Outline pattern: stat physics in olympiad mode
  • identify the relevant distribution or scaling law (you rarely need a full derivation) - estimate the dominant contribution region (what sets the scale?)
  • keep one dimensionless parameter to justify neglecting a term

D. Coupled Phenomena (Thermo Meets Waves)

  • IPhO 2019 T3 — “Thermoacoustic Engine” (PDF)
Outline pattern: coupled-process problems
  • separate the “thermo bookkeeping” part from the “dynamics” part - identify which coupling term is actually being tested - do one limiting-case check: coupling to zero should reduce to a known simpler model

E. Transport and Experimental Thermo

  • IPhO 2024 E1 — “Heat Conduction in a Copper Rod” (PDF)
  • IPhO 2019 E2 — “Wiedemann-Franz Law” (PDF)
Write-up pattern: transport experiments
  • decide your model form and what plot makes a slope equal the parameter - state boundary conditions and what you assume is constant (steady state vs transient) - identify the dominant systematic and whether it pushes results up or down

F. A Real-World Thermo Problem (Pressure, Phase, and Modelling)

  • IPhO 2025 T3 — “Champagne!” (PDF)
Outline pattern: real-world thermo modelling
  • write the simplest model first (ideal gas, constant temperature, quasi-static) - add one correction only if you can justify its size - sanity check with limiting cases and bounds (pressures cannot be negative; efficiencies have maxima)
Practice loop

Alternate: one second-law bounding problem and one transport/experiment section per week. Then continue via the IPhO Thermodynamics & Statistical Physics Hub.

Back to IPhO Problem Sets