Thermodynamics Formulas
A complete list of thermodynamics formulas, covering heat, specific heat, the ideal gas law, entropy, Carnot efficiency, and thermal expansion.
16 formulas. Use the interactive searcher to solve for any variable and convert units.
Open the interactive searcher →Heat energy
Q = m·c·ΔT
Q heat energyJm masskgc specific heat capacityJ/(kg·K)ΔT temperature changeK
Latent heat
Q = m·L
Q heat energyJm masskgL latent heatJ/kg
Ideal gas law
P·V = n·R·T
P pressurePaV volumem³n molesmolR gas constantJ/(mol·K)T temperatureK
Pressure
P = F / A
P pressurePaF forceNA aream²
Density
ρ = m / V
ρ densitykg/m³m masskgV volumem³
First law of thermodynamics
ΔU = Q − W
ΔU internal energy changeJQ heatJW workJ
Thermal expansion (linear)
ΔL = α·L₀·ΔT
ΔL length changemα expansion coefficient1/KL₀ original lengthmΔT temperature changeK
Thermal expansion (volume)
ΔV = β·V₀·ΔT
ΔV volume changem³β expansion coefficient1/KV₀ original volumem³ΔT temperature changeK
Heat conduction
Q/t = k·A·ΔT / L
Q heatJt timesk thermal conductivityW/(m·K)A aream²ΔT temperature differenceKL thicknessm
Carnot efficiency
η = 1 − T_c / T_h
η efficiencyT_c cold temperatureKT_h hot temperatureK
Entropy change
ΔS = Q / T
ΔS entropy changeJ/KQ heatJT temperatureK
Average KE of gas
KE = (3/2)·k_B·T
KE kinetic energyJk_B Boltzmann constantJ/KT temperatureK
RMS molecular speed
v_rms = √(3·k_B·T / m)
v_rms RMS speedm/sk_B Boltzmann constantJ/KT temperatureKm masskg
Work in isobaric process
W = P·ΔV
W workJP pressurePaΔV volume changem³
Stefan–Boltzmann law
P = σ·A·e·T⁴
P powerWσ Stefan-Boltzmann constantW/(m²·K⁴)A aream²e emissivityT temperatureK
Wien's displacement law
λ_max = b / T
λ_max peak wavelengthmb Wien constantm·KT temperatureK