🔥 Thermodynamics
Heat, temperature and energy transfer. Covers specific heat, gas laws, the laws of thermodynamics and heat engines.
What you will learn
- Distinguish heat from temperature
- Use the ideal gas law and calorimetry
- Apply the first and second laws of thermodynamics
- Evaluate heat engine efficiency
Study guide
Introductory College concepts
Blackbody Radiation — Why Hot Objects Glow and How Color Reveals Temperature
An ideal blackbody absorbs and emits perfectly. Learn Planck's resolution of the ultraviolet catastrophe, Wien's law, the Stefan–Boltzmann law, and how…
The Carnot Cycle in Detail — Four Steps to Maximum Efficiency
The Carnot cycle is the most efficient heat engine physics allows. Walk through its four reversible steps, derive the efficiency limit η = 1 − Tc/Th, and…
Entropy and the Second Law of Thermodynamics
Entropy and the second law of thermodynamics: why heat flows hot to cold, why perpetual motion is impossible, and what entropy really measures.
First Law of Thermodynamics — Energy Conservation Explained
Energy cannot be created or destroyed — the first law of thermodynamics, ΔU = Q − W. Learn sign conventions, internal energy, and real worked examples.
Kinetic Theory of Gases — Molecules, Pressure and Temperature
Kinetic theory explains gas pressure and temperature as trillions of molecular collisions. Derive P from molecular motion, meet v_rms, and see why…
High School concepts
Heat Engines — How They Work and Their Efficiency Limit
How heat engines turn fire into motion: the four-stroke cycle, steam turbines, Carnot's efficiency limit η = 1 − Tc/Th, and why waste heat is unavoidable.
Modes of Heat Transfer — Conduction, Convection and Radiation
Heat moves in exactly three ways: conduction through contact, convection through moving fluid, and radiation through empty space. Laws, examples and a…
Ideal Gas Law — PV = nRT Explained with Examples
PV = nRT unites pressure, volume, temperature and amount of gas in one equation. Learn each variable, when the law holds, and how to solve gas problems.
Phase Changes — Melting, Boiling and the Energy Hidden in Latent Heat
Why temperature stalls while ice melts or water boils: the six phase transitions, latent heat Q = mL, water's latent heats, and a worked melting calculation.
Specific Heat Capacity — Formula, Water's Value, and Uses
Specific heat capacity explains why water heats slowly and sand scorches fast. Master Q = mcΔT, water's 4186 J/(kg·K), and calorimetry basics.
Thermal Expansion — Why Bridges Have Gaps
Why bridges have gaps and power lines sag in summer: thermal expansion explained — ΔL = αL₀ΔT, expansion joints, and bimetallic strips.
Beginner concepts
Formulas
η = 1 − T_c/T_h — Carnot Efficiency Limit
Maximum efficiency equals one minus the cold reservoir temperature over the hot reservoir temperature.
Ideal Gas Law — PV = nRT
Pressure times volume equals moles times the gas constant times absolute temperature.
v_rms = √(3RT/M) — Root-Mean-Square Molecular Speed
RMS speed equals the square root of three R T over molar mass.
Specific Heat — Q = mcΔT
Heat transferred equals mass times specific heat times temperature change.
Thermal Efficiency — η = W/Qh
Thermal efficiency equals useful work output divided by heat input.
Calculators
Simulations
Practice
Heat Engines Practice
10 problems · 10 practice problems on heat engines, refrigerators and the Carnot efficiency limit.…
Entropy and Second Law Practice
10 problems · 10 practice problems on entropy and the second law — disorder, irreversibility and the arrow of time…
First Law of Thermodynamics Practice
10 problems · 10 practice problems on the first law of thermodynamics — internal energy, heat, work and energy con…
Gas Laws Practice
10 problems · 10 practice problems on gas laws — Boyle, Charles, and the ideal gas law PV = nRT.…
Heat Practice — Thermodynamics, Specific Heat and Gas Laws
10 problems · 10 practice problems on heat and thermodynamics — specific heat, the ideal gas law, heat engines and…
Heat Transfer Practice
10 problems · 10 practice problems on heat transfer — conduction, convection, radiation and thermal conductivity.…
Phase Changes Practice
10 problems · 10 practice problems on phase changes — melting, boiling, latent heat and heating curves.…