Constants library — formula.expert

Boltzmann constant exact

k_{\mathrm{B}} = 1.380649 \times 10^{-23}\ \text{J/K}

J/KThe energy per kelvin carried by a single particle's degree of freedom, fixed at exactly 1.380649e-23 J/K to define the kelvin.

Molar gas constant exact

R = 8.31446261815324\ \text{J/(mol}{\cdot}\text{K)}

J/(mol·K)The universal gas constant, R = k·N_A = 8.314462618 J/(mol·K), exact since 2019 and the R in PV = nRT and in every entropy table.

Stefan-Boltzmann constant exact

\sigma = 5.670374419 \times 10^{-8}\ \text{W/(m}^{2}{\cdot}\text{K}^{4}\text{)}

W/(m²·K⁴)Radiant emittance of a blackbody per fourth power of temperature: 5.670374419e-8 W/(m²·K⁴), exact in the post-2019 SI.

Wien displacement law constant (wavelength) exact

b = 0.002897771955\ \text{m}{\cdot}\text{K}

m·KWien's constant b = 2.897771955e-3 m·K: divide by absolute temperature to get the wavelength where a blackbody's spectrum peaks.

Wien displacement law constant (frequency) exact

b' = 5.878925757 \times 10^{10}\ \text{Hz/K}

Hz/KFrequency form of Wien's law, b' = 5.878925757e10 Hz/K: the peak frequency of a blackbody is b'·T, not c divided by the peak wavelength.

First radiation constant exact

c_1 = 3.741771852 \times 10^{-16}\ \text{W}{\cdot}\text{m}^{2}

W·m²c₁ = 2πhc² = 3.741771852e-16 W·m², the numerator of Planck's law in its spectral exitance form and the scale of all blackbody emission.

Second radiation constant exact

c_2 = 0.01438776877\ \text{m}{\cdot}\text{K}

m·Kc₂ = hc/k = 1.438776877e-2 m·K, the constant in the exponent of Planck's law and the basis of radiation thermometry.

Molar volume of an ideal gas at STP (0 °C, 100 kPa) exact

V_{\mathrm{m}}^{\,\mathrm{STP}} = 22.71095464\ \text{L/mol}

L/mol22.71095464 L/mol at IUPAC standard temperature and pressure, 273.15 K and 100 kPa exactly — not the older 22.4 L/mol.

Molar volume of an ideal gas at 0 °C and 1 atm exact

V_{\mathrm{m}}^{\,\mathrm{atm}} = 22.41396954\ \text{L/mol}

L/molThe textbook 22.414 L/mol: one mole of ideal gas at 273.15 K and 101.325 kPa, the pre-1982 definition of standard conditions.

Molar volume of an ideal gas at 25 °C and 1 atm exact

V_{\mathrm{m}}^{\,\mathrm{NTP}} = 24.4654037\ \text{L/mol}

L/mol24.4654 L/mol at 298.15 K and 101.325 kPa, the ambient reference used for gas concentrations in ppm-to-mg/m³ conversions.

Loschmidt constant exact

n_0 = 2.686780111 \times 10^{25}\ \text{m}^{-3}

m⁻³Number density of an ideal gas at 273.15 K and 101.325 kPa: 2.6867801e25 molecules per cubic metre, or 2.69e19 per cubic centimetre.

Sackur-Tetrode constant measured

S_0/R = -1.15170754\ \text{—}

—Reduced absolute entropy of an ideal monatomic gas at 1 K and 100 kPa, -1.1517075, the constant that puts Planck's h inside a classical gas.

Molar mass constant measured

M_{\mathrm{u}} = 0.00100000000105\ \text{kg/mol}

kg/molM_u = 1.00000000105e-3 kg/mol, the factor turning a relative atomic mass into a molar mass — no longer exactly 1 g/mol since 2019.

Standard atmosphere exact

p_{\mathrm{atm}} = 101,325\ \text{Pa}

PaOne standard atmosphere is exactly 101325 Pa, equal to 14.6959 psi, 760 mmHg, 29.921 inHg or 1.01325 bar, by international definition.

Standard state pressure exact

p^{\circ} = 100,000\ \text{Pa}

PaThe thermodynamic standard state pressure, exactly 1 bar = 100 kPa, the p° in every tabulated ΔG°, ΔH° and equilibrium constant.

Absolute zero exact

T = 0\ \mathrm{K} = 0\ \text{K}

KThe zero of the thermodynamic temperature scale: 0 K, equal to -273.15 °C and -459.67 °F exactly, both figures fixed by definition.

Ice point (0 °C in kelvin) exact

T_0 = 273.15\ \text{K}

KZero degrees Celsius is exactly 273.15 K, the offset that converts every Celsius reading to absolute temperature in gas-law work.

Triple point of water measured

T_{\mathrm{TPW}} = 273.16\ \text{K}

KThe unique 273.16 K (0.01 °C) at which ice, liquid water and vapour coexist — exact until 2019, now a measured value good to 0.1 mK.

Triple point pressure of water measured

p_{\mathrm{TPW}} = 611.657\ \text{Pa}

Pa611.657 Pa, about 0.6 % of an atmosphere: the vapour pressure at water's triple point and the floor below which liquid water cannot exist.

Normal boiling point of water

T_{\mathrm{b}} = 373.1243\ \text{K}

KWater boils at 99.9743 °C (373.1243 K) under one standard atmosphere — very slightly below 100 °C, and not by accident.

Specific gas constant for dry air

R_{\mathrm{air}} = 287.0528\ \text{J/(kg}{\cdot}\text{K)}

J/(kg·K)R/M for dry air, 287.0528 J/(kg·K), using the standard-atmosphere molar mass 28.9644 g/mol — the R in p = ρRT for air.

Specific gas constant for water vapour

R_{\mathrm{v}} = 461.523\ \text{J/(kg}{\cdot}\text{K)}

J/(kg·K)R/M for water vapour, 461.523 J/(kg·K), from a molar mass of 18.015268 g/mol — the constant behind psychrometrics and humidity ratio.

Heat capacity ratio of air

\gamma_{\mathrm{air}} = 1.4\ \text{—}

—γ = cp/cv = 1.400 for dry air near 20 °C and 1 atm, the exponent in adiabatic compression and in the speed of sound.

Heat capacity ratio of argon

\gamma_{\mathrm{Ar}} = 1.667\ \text{—}

—γ = 1.667 for argon and the other monatomic gases, the theoretical maximum 5/3 predicted by kinetic theory for point-like atoms.

Heat capacity ratio of steam

\gamma_{\mathrm{steam}} = 1.33\ \text{—}

—γ ≈ 1.33 for low-pressure steam at 100 °C: a triatomic bent molecule with rotational modes that lower it well below air's 1.40.

Specific heat capacity of liquid water

c_{p,\mathrm{water}} = 4181.6\ \text{J/(kg}{\cdot}\text{K)}

J/(kg·K)4181.6 J/(kg·K) for liquid water at 25 °C and 0.1 MPa — about 1.00 BTU/(lb·°F), the highest of any common liquid.

Specific heat capacity of ice

c_{p,\mathrm{ice}} = 2108\ \text{J/(kg}{\cdot}\text{K)}

J/(kg·K)About 2108 J/(kg·K) for ice at 0 °C, roughly half the value for liquid water — the reason freezers cool loads far faster than they freeze them.

Specific heat capacity of dry air

c_{p,\mathrm{air}} = 1005\ \text{J/(kg}{\cdot}\text{K)}

J/(kg·K)About 1005 J/(kg·K) at constant pressure for dry air near 300 K and 1 atm; cv is 718 J/(kg·K), and their ratio is γ = 1.40.

Latent heat of fusion of water

L_{\mathrm{f}} = 333,550\ \text{J/kg}

J/kg333.55 kJ/kg (143.4 BTU/lb) to melt ice at 0 °C without changing its temperature — equivalent to 80 K of sensible heating of water.

Latent heat of vaporisation of water

L_{\mathrm{v}} = 2,256,400\ \text{J/kg}

J/kg2256.4 kJ/kg (970 BTU/lb) to boil water at 100 °C and 1 atm, nearly seven times the heat of fusion and the basis of all steam heating.

Maximum density of water (4 °C) measured

\rho_{\max} = 999.975\ \text{kg/m}^{3}

kg/m³Water is densest at about 3.98 °C, 999.975 kg/m³ — the anomaly that makes ice float and keeps deep lakes from freezing solid.

Density of water at 20 °C measured

\rho_{20} = 998.207\ \text{kg/m}^{3}

kg/m³998.207 kg/m³ at 20 °C and 1 atm (62.316 lb/ft³), the reference density behind specific gravity and most laboratory calibrations.

Mechanical equivalent of heat exact

J = 4.1868\ \text{J/cal (IT)}

J/cal (IT)4.1868 joules per international-table calorie, exact by definition — the conversion Joule spent two decades measuring by hand.

Calorie (thermochemical) exact

\mathrm{cal} = 4.184\ \text{J}

JThe thermochemical calorie is exactly 4.184 J; the food Calorie is a kilocalorie, 4184 J, a factor of a thousand larger.

British thermal unit exact

\mathrm{BTU} = 1055.05585262\ \text{J}

JThe international-table BTU is exactly 1055.05585262 J, the heat that raises one pound of water by one degree Fahrenheit.

Ton of refrigeration exact

\mathrm{TR} = 3516.8528420667\ \text{W}

WExactly 12000 BTU/h = 3516.85 W: the cooling rate that melts one short ton of ice in 24 hours, still the unit chillers are sold in.

Boiler horsepower

\mathrm{bhp} = 9809.5\ \text{W}

W9809.5 W (33475 BTU/h): the heat rate to evaporate 34.5 lb/h of water at 212 °F, and nothing at all to do with mechanical horsepower.

Thermodynamic constants

Thermodynamic 37