Topic Cluster

Thermodynamics

Thermodynamics: heat, temperature, entropy and energy transfer — the science of engines, refrigerators and the universe’s arrow of time.

Thermodynamics — the core equations of thermodynamics, and every article on the topic
The equations this topic keeps coming back to.

What Is Thermodynamics?

Thermodynamics is the physics of heat, temperature and energy transfer in systems made of enormous numbers of particles — where entropy emerges from the statistics of countless tiny collisions.

Core equations in thermodynamics
RelationshipEquationWhat it tells you
Specific heatQ = m·c·ΔTEnergy to change a temperature
Latent heatQ = m·LEnergy to change a state
First lawΔU = Q − WEnergy conservation for a gas
Ideal gas lawP·V = n·R·TState of an ideal gas
Carnot efficiencyη = 1 − Tc / ThBest possible heat-engine efficiency
Entropy changeΔS = Q / TDisorder gained in a reversible step
Energy Transfers in Physics: Stores and Pathways
Thermodynamics

Energy Transfers in Physics: Stores and Pathways

Energy is held in stores and moved by pathways, and an energy transfer names three things: the store the joules leave, the pathway they take and the store they arrive in. There are four pathways - mechanically, electrically, by heating and by radiation - and a single machine rarely uses more than three of them, because a pathway can be named and still carry nothing. The branch that matters most is the one nobody measures: add up every branch you can name, deduct them from the supply, and the remainder went to the surroundings. That balance reads zero because it was built to, which is the method rather than a coincidence. This page defines stores and pathways, builds the account for a kettle and a winch branch by branch, draws it as a Sankey diagram, and works eight problems step by step.

22 min read
Adiabatic Process Explained
Thermodynamics

Adiabatic Process Explained

An adiabatic process runs with no heat crossing the boundary, so the work you do on a gas has nowhere to go but into its own internal energy - which is why a fast squeeze heats and a fast expansion cools. This page gives the relation P V^gamma = constant and its two equivalent forms, shows where gamma comes from by counting a molecule's degrees of freedom, and then answers the question our isothermal and Carnot pages leave open: an adiabat is steeper than an isotherm by exactly gamma. Seven worked problems, two original diagrams, an interactive lab and a calculator.

20 min read
Kinetic Theory of Gases
Thermodynamics

Kinetic Theory of Gases

The kinetic theory of gases gets the pressure of a gas out of nothing but the mass and speed of its molecules, in the equation PV = (1/3) N m v_rms^2. This page derives it, explains where the one third comes from, substitutes it into PV = NkT, and then answers the question the equation raises: how fast is a gas molecule? There are three defensible answers - the most probable, mean and rms speeds - and this page works all three out for five gases. Seven worked problems, two original diagrams, an interactive lab and a calculator.

20 min read
Energy Conversion Examples: Where the Joules Actually Go
Thermodynamics

Energy Conversion Examples: Where the Joules Actually Go

Energy conversion is the same joules changing form without changing total, and this guide traces fourteen of the commonest conversions from one end to the other. It covers the one bookkeeping line every conversion obeys, how to write a conversion chain and why every chain is really a tree, five everyday examples from a torch to a phone, the four routes a power station can take to the same electricity, and where the energy that looks lost has actually gone, with two original diagrams, seven worked problems and an interactive lab.

21 min read
Isothermal Process: What It Is and How to Find the Work
Thermodynamics

Isothermal Process: What It Is and How to Find the Work

An isothermal process holds the temperature still while the volume changes, so an ideal gas travels the curve PV = nRT and the work it does is the area underneath: W = nRT ln(V2/V1). One mole at 300 K doubling from 10.0 L to 20.0 L does 1728.8 J of work and draws in the same 1728.8 J as heat; let it expand freely into a vacuum between the same two states and it does none of it, while the entropy change stays at 5.763 J/K. Eight worked problems, three original diagrams, an interactive lab and a calculator.

23 min read
Thermal Diffusivity: How Fast Heat Really Moves Through a Material
Thermodynamics

Thermal Diffusivity: How Fast Heat Really Moves Through a Material

Thermal diffusivity is how fast a temperature change travels through a material, alpha = k divided by rho c, and it answers the question conductivity cannot: how long. A wall twice as thick takes four times as long to warm right through, still air outruns stainless steel, and a third quantity built from the same three properties decides why metal feels colder than wood. Eight worked problems, three original diagrams, an interactive lab and a calculator.

20 min read
The Combined Gas Law: When Pressure and Temperature Both Move
Thermodynamics

The Combined Gas Law: When Pressure and Temperature Both Move

The combined gas law reads PV = nRT twice - once before a change and once after - with the amount of gas held fixed, which leaves P1V1/T1 = P2V2/T2. Boyle, Charles and Gay-Lussac each hold one quantity still; this relation holds none of them. Eight worked problems, three original diagrams, an interactive simulator, and the two input mistakes that quietly produce plausible wrong answers: Celsius fed into a ratio, and gauge pressure.

21 min read