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Converting between equivalent quantities

This package extends the uconvert and ustrip functions from Unitful.jl to accept an additional argument of type Equivalence. Supplying this argument allows converting between units of different dimensions that are linked by the specified equivalence, e.g., the mass–energy equivalence $E=mc^2$:

julia> using Unitful, UnitfulEquivalences

julia> uconvert(u"keV", 1u"me", MassEnergy()) # electron rest mass is equivalent to ≈511 keV
510.9989499961642 keV

julia> ustrip(u"keV", 1u"me", MassEnergy())
510.9989499961642

The equivalences MassEnergy, Spectral, and Thermal are defined and exported by this package:

UnitfulEquivalences.MassEnergy — Type
MassEnergy()

Equivalence to convert between mass and energy according to the relation $E = mc^2$, where

  • $E$ is the energy,
  • $m$ is the mass and
  • $c$ is the speed of light in vacuum.

Example

julia> uconvert(u"keV", 1u"me", MassEnergy()) # electron rest mass is equivalent to ≈511 keV
510.9989499961642 keV
source
UnitfulEquivalences.Spectral — Type
Spectral(; frequency=:linear, wavelength=:linear, wavenumber=:linear)

Equivalence that relates the energy of a photon to its (linear or angular) frequency, wavelength, and wavenumber. Whether to convert to linear or angular quantities is determined by optional keyword arguments, :linear is the default for all quantities.

Equivalent quantities are converted according to the relations $E = hf = ħω = hc/λ = ħc/ƛ = hcν̃ = ħck$, where

  • $E$ is the photon energy,
  • $f$ is the (temporal) frequency (frequency=:linear),
  • $ω$ is the angular frequency (frequency=:angular),
  • $λ$ is the wavelength (wavelength=:linear),
  • $ƛ$ is the angular (also called reduced) wavelength (wavelength=:angular),
  • $ν̃$ is the spectroscopic wavenumber (wavenumber=:linear),
  • $k$ is the angular wavenumber (wavelength=:angular),
  • $h$ is the Planck constant,
  • $ħ$ is the reduced Planck constant and
  • $c$ is the speed of light in vacuum.

Examples

julia> uconvert(u"nm", 13.6u"eV", Spectral()) # photon wavelength needed to ionize hydrogen
91.16485178911785 nm

julia> uconvert(u"Hz", 589u"nm", Spectral(frequency=:angular)) # angular frequency of sodium D line
3.1980501991661345e15 Hz
source
UnitfulEquivalences.Thermal — Type
Thermal()

Equivalence to convert between temperature and energy according to the relation $E = kT$, where

  • $E$ is the energy,
  • $T$ is the temperature and
  • $k$ is the Boltzmann constant.

Example

julia> uconvert(u"eV", 20u"°C", Thermal()) # room temperature is equivalent to ≈1/40 eV
0.025261712457978588 eV
source

API

Unitful.uconvert — Function
uconvert(u::Units, x::Quantity, e::Equivalence)

Convert x to the units u (of different dimensions) by using the specified equivalence.

Examples

julia> uconvert(u"keV", 1u"me", MassEnergy()) # electron rest mass is equivalent to ≈511 keV
510.9989499961642 keV

julia> uconvert(u"eV", 589u"nm", Spectral()) # photon energy of sodium D₂ line (≈589 nm)
2.104994880020378 eV
source
Unitful.ustrip — Function
ustrip([T::Type,] u::Units, x::Quantity, e::Equivalence)

Convert x to the units u (of different dimensions) by using the specified equivalence and return the numeric value of the resulting quantity. If T is supplied, also convert the resulting number to type T.

Examples

julia> ustrip(u"keV", 1u"me", MassEnergy()) # electron rest mass is equivalent to ≈511 keV
510.9989499961642

julia> ustrip(u"eV", 589u"nm", Spectral()) # photon energy (in eV) of sodium D₂ line
2.104994880020378
source