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IEC 60364-5-54 gives the following formula for the calculation of the factor k:
where Qc = volumetric heat capacity of conductor at 20°C, J.K-1.mm-3
ß = reciprocal of temperature coefficient of resistivity at 0 °C
ρ20 = electrical resistivity of conductor material at 20 °C, Ω.mm
ϴi = initial temperature of the conductor, °C
ϴf = final temperature of the conductor, °C
Note: strictly speaking ß is specified at 0 °C. Within myCableEngineering calculations, ß is determined by taking the reciprocal of the 20 °C temperature coefficient. This introduces a small, but negligible error.
For manual calculations, the following will give realistic results:
Substituting the above values and rearranging the IEC equation slightly, gives:
k=226 ln( 1+ θ f − θ i 234.5+ θ i ) - copper conductors
k=148 ln( 1+ θ f − θ i 228+ θ i ) - aluminium conductors
k=78 ln( 1+ θ f − θ i 202+ θ i ) - steel