Fundamentals of ThermodynamicsAn Interactive Course

How this course works

Each lesson opens with one question and builds the intuition to answer it before formalising anything. Along the way you will find:

• Live explorables. More than thirty interactive simulations — a box of bouncing molecules that measures its own pressure, a pot of water you can boil at the top of Everest, a Carnot engine you can run backwards, a steam plant you can rebuild from 1900 to today, a heat pump, a cooling tower and a flame that refuses to burn completely. Predict first, then drag.
• Real property data. Behind every widget sit the course's own steam tables — saturation curves to within 0.1% of the IAPWS standard — plus refrigerant, ideal-gas and moist-air properties, so the numbers you see are the numbers an engineer would use.
• Pause and ponder. Questions worth a minute of thought before you reveal the answer.
• Check your intuition. Short quizzes whose explanations are often the best part.
• Watch the idea. Many simulations have a narrated tour that moves the sliders for you. Press it, then take the controls.
• Challenges. Small goals under the simulations ("can you make a heat pump deliver four units of heat for one of work?") that tick themselves off when you succeed.
• Estimate first. Before a big number is revealed, you guess it on a logarithmic scale.
• Going deeper. The equations engineers actually use, colour-coded to match the pictures: $\cheat{Q}$ for heat is always red, $\cwork{W}$ for work always gold, $\cent{S}$ for entropy always purple and $\cex{E}$ for exergy always pink.
• Dotted words are defined on hover — the full glossary is at the bottom of this page.

Throughout the course, colours mean the same thing everywhere:

• The Power Plant Studio. The course ends with a capstone: take a brief — a grid power station, a district-heating plant, a heat pump for a town — and design the system that wins on efficiency, cost of fuel and emissions.

What you will be able to do

• Define a system, its state and its properties, and use pressure and temperature correctly — absolute, gauge, kelvin
• Apply the first law to closed systems, cycles and control volumes: turbines, pumps, nozzles, heat exchangers, throttles, filling tanks
• Read steam and refrigerant tables, and know when the ideal-gas model is good enough
• Use the second law to find the best any device can do — and entropy to measure how far short of it a real device falls
• Do an exergy analysis that shows where a system's real losses are
• Analyse and improve Rankine, Brayton, Otto, Diesel, combined and vapour-compression cycles
• Work with moist air, combustion and chemical equilibrium

Prerequisites

Algebra, a little calculus and first-year physics. No prior thermodynamics is assumed.

A note on the approach

The course follows the arc of Michael Moran and Howard Shapiro's Fundamentals of Engineering Thermodynamics (with Boettner and Bailey in later editions), the standard text on which a generation of engineers learned the subject: its chapter order, its sign conventions (work done by the system and heat added to it are positive) and its emphasis on careful problem solving and on exergy. Worked numbers are checked against the book's examples wherever they overlap; the course's own steam tables reproduce its ideal Rankine cycle (Example 8.1) to three significant figures.

Three threads run through it: energy is conserved, entropy is not, and exergy tells you which losses matter.

The property models are compact approximations: saturation curves fitted to the IAPWS formulations, a cubic equation of state for superheated and compressed states (within about 1.5% of the steam tables), and ideal gases with vibrating molecules. They are built for intuition and good engineering estimates, not for certifying a power plant.

Glossary

SystemLesson 1

Whatever we choose to study, separated from its surroundings by a boundary. A closed system (control mass) exchanges no mass; an open system (control volume) does.

PropertyLesson 1

A characteristic of a system at a given state — pressure, temperature, volume, energy — that does not depend on how the state was reached.

StateLesson 1

The condition of a system, described by its properties. For a simple compressible substance, two independent intensive properties fix the state.

EquilibriumLesson 1

A state with no tendency to change on its own: no unbalanced forces, temperature differences or chemical driving forces.

Quasi-equilibrium processLesson 1

A process slow enough that the system passes through a continuous sequence of equilibrium states — the idealisation that lets us draw processes as lines on diagrams.

Absolute and gauge pressureLesson 1

Absolute pressure is measured from a perfect vacuum; gauge pressure is the excess over the local atmosphere. Thermodynamics always uses absolute pressure.

Zeroth lawLesson 1

Two bodies each in thermal equilibrium with a third are in thermal equilibrium with each other — the principle that makes thermometers possible.

Kelvin scaleLesson 1

The absolute temperature scale. Its zero is where the pressure of an ideal gas at constant volume would extrapolate to zero: −273.15 °C.

WorkLesson 2

Energy transferred across a boundary that could, in principle, have raised a weight. Expansion work is ∫p dV — the area under a process on a p–V diagram.

HeatLesson 2

Energy transferred across a boundary because of a temperature difference. Like work, it is a transfer, not a property — a system has energy, not heat.

First lawLesson 2

Energy is conserved: for a closed system, ΔE = Q − W. Energy can change form and cross boundaries, but never appears or disappears.

Internal energy ULesson 2

The energy stored in the molecules of a system: their motion, rotation, vibration and the forces between them.

Polytropic processLesson 2

A process obeying pVⁿ = constant: n = 0 at constant pressure, n = 1 isothermal for an ideal gas, n = γ adiabatic and reversible, n → ∞ at constant volume.

Thermal efficiencyLesson 2

Net work out divided by heat in, η = W_cycle/Q_in, for a power cycle.

Coefficient of performanceLesson 2

Useful heat moved divided by work in: Q_C/W for a refrigerator, Q_H/W for a heat pump. It can exceed 1.

Quality xLesson 3

The mass fraction of vapour in a saturated liquid–vapour mixture, from 0 (saturated liquid) to 1 (saturated vapour).

SaturationLesson 3

The conditions at which liquid and vapour coexist. At a given pressure there is one saturation temperature: the boiling point.

Critical pointLesson 3

The top of the vapour dome — for water 374 °C and 220.6 bar — above which liquid and vapour can no longer be told apart.

Enthalpy hLesson 3

h = u + pv: internal energy plus the flow work needed to push the fluid in or out. The natural energy property for flowing streams.

Specific heats c_v, c_pLesson 3

The energy needed to raise a unit mass by one degree at constant volume or pressure. For gases they rise with temperature as molecular vibrations wake up.

Ideal gasLesson 3

A gas obeying pv = RT, with energy depending on temperature only. Accurate when the pressure is low compared with the critical pressure or the temperature is high.

Compressibility factor ZLesson 3

Z = pv/RT. Equal to 1 for an ideal gas; it measures how far a real gas departs from ideal behaviour.

Control volumeLesson 4

A region of space through which mass flows. Mass and energy balances are written for the region, not for a fixed lump of matter.

Flow workLesson 4

The work pv per unit mass needed to push fluid into or out of a control volume — the reason enthalpy, not internal energy, appears in flow balances.

Steady stateLesson 4

Nothing inside the control volume changes with time: mass and energy in equal mass and energy out.

ThrottlingLesson 4

A flow through a restriction — a valve or porous plug — with no work and negligible heat transfer, so h stays the same while the pressure drops.

Kelvin–Planck statementLesson 5

No cycle can produce net work while exchanging heat with a single reservoir. Every heat engine must reject heat.

Clausius statementLesson 5

Heat cannot flow from a colder to a hotter body without some other effect — such as work input.

Reversible processLesson 5

An idealised process that could be undone leaving no trace on system or surroundings. Friction, heat transfer across a finite ΔT, mixing and unrestrained expansion all make processes irreversible.

Carnot efficiencyLesson 5

The maximum efficiency of any power cycle between reservoirs at T_H and T_C: η = 1 − T_C/T_H, temperatures in kelvin.

Entropy SLesson 6

A property defined by dS = (δQ/T)_rev. It measures how energy is spread across a system’s microscopic states, and the entropy of an isolated system can only increase.

Entropy generation σLesson 6

The entropy produced inside a system by irreversibilities. Always ≥ 0, and zero only for reversible processes.

Isentropic efficiencyLesson 6

How close a turbine, compressor, pump or nozzle comes to the ideal (adiabatic, reversible) process between the same pressures.

ExergyLesson 7

The maximum useful work obtainable as a system comes into equilibrium with its environment. Unlike energy, exergy is destroyed by irreversibilities.

Dead stateLesson 7

The system at the temperature and pressure of the environment (T₀, p₀), where its exergy is zero.

Exergy destructionLesson 7

Exergy lost to irreversibility: E_d = T₀σ (the Gouy–Stodola theorem).

Rankine cycleLesson 8

The ideal cycle of a steam power plant: pump, boiler, turbine, condenser.

ReheatLesson 8

Returning partly expanded steam to the boiler before further expansion, raising efficiency and keeping the turbine exhaust dry.

RegenerationLesson 8

Using steam bled from the turbine to preheat feedwater, so heat is added at a higher average temperature.

Back work ratioLesson 8

The fraction of the turbine work consumed by the pump or compressor: about 1% in a steam plant, 40–60% in a gas turbine.

Brayton cycleLesson 9

The ideal cycle of a gas turbine: compressor, combustor (constant pressure), turbine, heat rejection (constant pressure).

Otto cycleLesson 9

The ideal cycle of a spark-ignition engine, with heat added at constant volume. Its efficiency depends only on the compression ratio.

Diesel cycleLesson 9

The ideal cycle of a compression-ignition engine, with heat added at constant pressure.

Combined cycleLesson 9

A gas turbine whose hot exhaust raises steam for a steam turbine, reaching efficiencies above 60%.

Vapour-compression cycleLesson 10

The cycle of almost every refrigerator and heat pump: compressor, condenser, expansion valve, evaporator.

Maxwell relationsLesson 11

Equalities between partial derivatives — such as (∂s/∂p)_T = −(∂v/∂T)_p — that let unmeasurable properties be computed from measurable ones.

Clapeyron equationLesson 11

dp_sat/dT = h_fg/(T v_fg): the slope of the saturation curve is set by the latent heat.

Joule–Thomson coefficientLesson 11

μ_J = (∂T/∂p)_h: how much a gas cools (μ > 0) or warms (μ < 0) when throttled.

Humidity ratio ωLesson 12

Mass of water vapour per unit mass of dry air.

Relative humidity φLesson 12

The partial pressure of water vapour divided by the saturation pressure at the same temperature.

Dew pointLesson 12

The temperature at which moist air becomes saturated when cooled at constant pressure and humidity ratio — where dew or condensation forms.

Wet-bulb temperatureLesson 12

The temperature a wetted thermometer reaches as water evaporates from it; the lowest temperature evaporative cooling can reach.

Stoichiometric (theoretical) airLesson 13

Exactly enough air to burn all the fuel completely, with no oxygen left over.

Heating valueLesson 13

The heat released by complete combustion of a unit of fuel. The higher heating value counts the water in the products as liquid, the lower as vapour.

Adiabatic flame temperatureLesson 13

The temperature the products reach if all the chemical energy goes into heating them.

Gibbs function GLesson 14

G = H − TS. At fixed temperature and pressure, a system reaches equilibrium where G is a minimum.

Equilibrium constant KLesson 14

K(T) = exp(−ΔG°/RT): fixes the balance between reactants and products at equilibrium. It depends on temperature only.

DissociationLesson 14

The breaking apart of products such as CO₂ and H₂O at high temperature, which stores energy and limits flame temperatures.