Mini Physics
Part of Mini EducationSwitch subject
SearchBookmarksMenu

First-year university thermodynamics

Learn University Year 1 thermodynamics through the laws, processes, engines, kinetic theory and heat transfer, with links to extension lessons.

  • University Physics Year 1
  • 40 lessons
Start topic

Before you begin

Thermodynamics links the state of a system to energy transfers and the limits on possible processes. Begin with a clear boundary: which matter is the system, what can cross the boundary, and which quantities describe the starting and final states?

Build on: A-Level thermal physics, energy conservation, the mole concept and basic differentiation and integration. Temperature ratios use kelvin; temperature differences can use kelvin or Celsius consistently.

Learning goals
  • Apply heat, work, internal-energy, and first-law accounting consistently across processes.
  • Model thermodynamic states using temperature, equations of state, and microscopic assumptions.
  • Analyse cycles, entropy constraints, engines, refrigerators, and limiting efficiencies.

Lessons

Work through them in order.

  1. Thermal energy and heatDistinguish thermal energy from heat and solve heat-exchange balances with consistent signs.
  2. The ideal gas equation of stateApply the ideal-gas equation of state, state its assumptions and judge when it breaks down.
  3. Heat capacityUse heat capacity, specific heat and latent heat to solve heating and cooling problems.
  4. Heat capacities of gasesDerive gas heat capacities at constant volume and pressure and show that Cₚ - CV = R.
  5. Heat capacity of solidsDerive the Dulong–Petit limit from lattice vibrations and explain why solid heat capacity falls at low temperature.
  6. Isochoric and isobaric processesApply the first law to constant-volume and constant-pressure processes of an ideal gas.
  7. Isothermal processesDerive the work in an isothermal ideal-gas process and relate the heat transferred to it.
  8. Adiabatic processesDerive the adiabatic relation PV^γ = constant for an ideal gas and link temperature change to work.
  9. The Carnot engineDerive the Carnot efficiency and use it as the upper limit for an engine between two temperatures.
  10. Heat-engine efficiencyCalculate the thermal efficiency of engines and the coefficient of performance of heat pumps.
  11. Heat pumps and refrigeratorsModel refrigerators and heat pumps as reversed engines and calculate their COP in each mode.
  12. The zeroth law of thermodynamicsUse the zeroth law to define temperature and justify how thermometers work.
  13. Heat engines and heat pumpsSet up the energy balance of heat engines and heat pumps over one cycle with clear sign conventions.
  14. The second law of thermodynamicsState the Kelvin–Planck and Clausius forms of the second law and show they are equivalent.
  15. Thermodynamic cyclesApply the first law to a closed cycle and read net work and cycle direction from a PV diagram.
  16. Reversible and irreversible thermodynamic processesDistinguish reversible from irreversible processes and explain why reversible paths set ideal limits.
  17. Kinetic temperatureDerive gas pressure from molecular motion and define temperature through mean kinetic energy.
  18. R.m.s. speed of gas particlesDerive the r.m.s. speed of gas molecules from temperature and interpret its size.
  19. The Maxwell–Boltzmann distributionRead the Maxwell–Boltzmann speed distribution, compare its characteristic speeds and see how temperature shifts it.
  20. Mean free pathDerive the mean free path, collision time and collision frequency of molecules in a dilute gas.
  21. Counting molecular degrees of freedomCount translational, rotational and vibrational modes for monatomic and diatomic gases.
  22. The Boltzmann distributionUse the Boltzmann factor, with degeneracy, to compare the populations of energy states.
  23. Limits of classical equipartitionExplain why classical equipartition fails for heat capacities and how frozen quantum modes resolve it.
  24. Thermal conductionApply Fourier's law of conduction and treat a conducting layer as a thermal resistance.
  25. Thermal conduction through layered materialsFind steady heat flow through layered slabs and cylindrical insulation with thermal resistances.
  26. How a temperature gradient developsExplain how a temperature gradient develops along a bar and settles to a linear steady state.
  27. Thermal convectionUse Newton's law of cooling and interpret the convection coefficient.
  28. Convective heat transferCombine convection and wall conduction in a thermal-resistance network to find heat flow.Supporting
  29. Thermal radiationApply the Stefan–Boltzmann law with emissivity to find net radiative heat exchange.
  30. Waste heat and the Carnot limitUse the Carnot limit to estimate the unavoidable waste heat of a real power plant.
  31. Measuring temperatureCalibrate a thermometer from a thermometric property using a two-point calibration.
  32. Temperature scalesConvert between Celsius, kelvin, Fahrenheit and Rankine using fixed points.
  33. Internal energy and state variablesExplain what internal energy includes, why it is a state variable and how it differs for gases and solids.
  34. Work done by gas pistonsDerive the pressure–volume work of a gas in a piston and fix its sign for expansion and compression.
  35. Why heat is a path variableShow that heat depends on the path by comparing two processes between the same states.
  36. Why thermodynamic work is a path variableFind work as the area under a PV curve and show that it depends on the path taken.
  37. Thermodynamic systems, heat and workDefine system, surroundings, heat and work, and separate state variables from path variables.
  38. The first law of thermodynamicsState the first law in differential and finite forms and apply it with consistent signs.
  39. The equipartition theoremUse equipartition and degree-of-freedom counting to predict internal energy and heat capacity.
  40. Thermal expansionDerive and apply the linear and volume expansion formulas and interpret expansion coefficients.

Practise and check

Recommended nextThermodynamics topic check

Topic reference

Connect state, process and microscopic model

A state relation such as the ideal gas law connects pressure, volume, temperature and amount. It does not determine heat or work. The first law accounts for energy transferred along a path; heat capacities tell you how the stored energy and required heat change under specified constraints. Keep the work convention explicit, and use an integral when a property changes across the interval.

Energy conservation alone does not decide whether a cycle can run as proposed. The second law constrains spontaneous transfer and sets limits on engines and heat pumps. Reversible models describe limiting behaviour; a real device also has losses and finite transfer rates. A claimed efficiency needs both its energy balance and its second-law bound.

Kinetic and statistical models explain how molecular motion and available quantum states produce pressure, internal energy and heat capacity. Transfer models then explain rates: conduction, convection and radiation describe how quickly energy crosses a boundary. Choose each model from its physical assumptions, rather than treating formulas from different situations as interchangeable.

Check a calculation against its model

State the fixed quantities and work channels before substituting numbers. Check units and transfer signs, and interpret the final phase as well as the temperature when latent heat is involved. Then test a relevant limit or an energy balance. If a gas is dense, a capacity varies, or a process is not quasistatic, identify the approximation that needs revision.

Further reading

Planck radiation law and Wien’s law develops the quantum spectrum underlying thermal radiation.