# Temperature in Kelvin to keV Conversion

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Practicing astrophysicists routinely refer to temperatures in units of eV or keV, even though this is wrong, because temperature is not dimensionally equivalent to energy. Nevertheless, they still do it, with the Boltzmann constant being implicitly included in the conversion. Here are formulas for temperature in Kelvin to keV conversion.

\[

E({\rm eV}) = \frac{kT}{e}

\]

because 1 eV is by definition the energy required to move a charge $e$ through a potential difference of 1 volt and is equal to $1.6 \times 10^{-19} \times 1$ Joules. Thus

\[

T \ ({\rm eV}) = 8.625 \times 10^{-5} \ T \ ({\rm Kelvin})

\]

and

\[

T \ ({\rm keV}) = 8.625 \ \times 10^{-4} \left(\frac{T \ ({\rm Kelvin})}{10^{4}

\ {\rm Kelvin}} \right)

\]

where $k=1.3806504 \times 10^{-23}$ Joules/Kelvin is the Boltzmann constant (source: NIST).

Details:

With $k=1.38 \times 10^{-23} \ \rm J \ K^{-1}$, $kT({\rm Kelvin})$ is in Joules, divide by the electron charge, $e$, to get eV, then divide by 1000 to get keV:

\[

\frac{k}{1000 e} = \frac{1.38 \times 10^{-23}}{1000 \times 1.6 \times 10^{-19}} = 8.625 \times 10^{-8}

\]