Thermodynamics & Heat

Heat, temperature, gas laws and the laws of thermodynamics

Thermodynamics & Heat brings together the key formulas that describe how energy moves, how gases behave, and how temperature changes affect matter. It’s a useful reference for students, exam revision, and anyone applying physics in real-world settings like engineering, chemistry, and HVAC, where understanding heat transfer and gas laws is essential for accurate calculations and practical problem-solving.

Heat Energy

Q = mc\Delta T

Heat needed to change a substance’s temperature.

Latent Heat

Q = mL

Heat for a phase change at constant temperature.

Ideal Gas Law

PV = nRT

Relates pressure, volume, moles and temperature.

Boyle's Law

P_1 V_1 = P_2 V_2

Pressure and volume are inversely related at constant T.

Charles's Law

\frac{V_1}{T_1} = \frac{V_2}{T_2}

Volume is proportional to temperature at constant P.

Gay-Lussac's Law

\frac{P_1}{T_1} = \frac{P_2}{T_2}

Pressure is proportional to temperature at constant V.

Combined Gas Law

\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}

Combines Boyle, Charles and Gay-Lussac.

First Law of Thermodynamics

\Delta U = Q - W

Energy conservation for a thermodynamic system.

Carnot Efficiency

\eta = 1 - \frac{T_C}{T_H}

Maximum efficiency of a heat engine.

Entropy Change

\Delta S = \frac{Q}{T}

Reversible entropy change at temperature T.

Linear Thermal Expansion

\Delta L = \alpha L_0 \Delta T

Length change of a solid when heated.

Heat Conduction (Fourier)

Q = \frac{kA\Delta T\,t}{d}

Heat conducted through a slab over time.

Celsius to Fahrenheit

F = \tfrac{9}{5}C + 32

Convert Celsius to Fahrenheit.

Celsius to Kelvin

K = C + 273.15

Convert Celsius to Kelvin.

RMS Molecular Speed

v_{rms} = \sqrt{\frac{3RT}{M}}

Root-mean-square speed of gas molecules.

Average KE of a Gas Molecule

\bar{E} = \tfrac{3}{2}k_B T

Mean translational kinetic energy per molecule.

Coefficient of Performance

COP = \frac{Q_C}{W}

Efficiency measure of a refrigerator or heat pump.