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Thermodynamics: Formula Cheat Sheet
Every key formula for Thermodynamics, with what it means and where it comes from.
| Formula | What it means | Topic |
|---|---|---|
| delta S = Q_rev / T | Change in entropy for a reversible heat transfer Q_rev at absolute temperature T. | Entropy Explained |
| delta S >= 0 | Second law: total entropy of an isolated system never decreases. | Entropy Explained |
| Q/t = k A delta T / d | Rate of conduction through a slab of conductivity k, area A, thickness d, temperature difference delta T. | Heat Transfer: Conduction, Convection, Radiation |
| P = epsilon sigma A T^4 | Radiated power, with emissivity epsilon, Stefan-Boltzmann constant sigma = 5.67 x 10^-8 W/m^2 K^4, and absolute temperature T. | Heat Transfer: Conduction, Convection, Radiation |
| Q = m c delta T | Heat needed to change temperature, with specific heat capacity c. | Temperature, Heat and Thermal Energy |
| T(K) = T(C) + 273.15 | Converting a Celsius temperature to kelvin. | Temperature, Heat and Thermal Energy |
| eta = 1 - Tc / Th | Maximum efficiency of a heat engine, with hot and cold reservoir temperatures in kelvin. | The Carnot Cycle and Heat Engines |
| eta = W / Qh | Efficiency equals work output divided by heat taken in. | The Carnot Cycle and Heat Engines |
| eta = 1 - Qc / Qh | Efficiency in terms of heat taken in Qh and heat rejected Qc. | The Carnot Cycle and Heat Engines |
| delta U = Q - W | Change in internal energy equals heat added minus work done by the system. | The First Law of Thermodynamics |
| delta U = Q + W | Same law with the other sign convention, where W is work done on the system. | The First Law of Thermodynamics |
| P V = n R T | Ideal gas law: pressure times volume equals moles times gas constant times absolute temperature. | The Ideal Gas Law |
| P V = N k_B T | Same law with number of particles N and Boltzmann constant k_B = 1.38 x 10^-23 J/K. | The Ideal Gas Law |
| P1 V1 / T1 = P2 V2 / T2 | Combined gas law, comparing one state with another at fixed amount of gas. | The Ideal Gas Law |
| ΔU = Q − W | Energy is conserved: heat added either raises the internal energy or leaves as work, and ΔU can be negative. | First Law of Thermodynamics Calculator |
| P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂ | For a fixed amount of gas, pressure times volume divided by absolute temperature stays constant through any change. | Gas Laws Calculator |
| P × V = n × R × T | For an ideal gas, pressure times volume equals the amount of gas times the gas constant times absolute temperature. | Ideal Gas Law Calculator |
| Q = m × c × ΔT | The heat needed to change a substance's temperature depends on its mass, its specific heat and the temperature change. | Specific Heat Calculator |
| ΔL = α × L₀ × ΔT | A solid expands in proportion to its original length, its expansion coefficient and the temperature rise. | Thermal Expansion Calculator |