TL;DR: What's the origin of the 10 degrees Celsius rule?

I have heard many times that for every 10 degrees Celsius, the lifespan of components gets halved. There are many documents on the web quoting that number.

But it seems too general to be taken at face value.

When I try to find literature on the topic, I come up with two things:

  • it's either too complex for me to understand.
  • it's written by someone that understands as much, or less, than me.
  • or, mostly, it's summed up as: high temperatures are bad, buy our solution.

I believe that the truth is probably a lot more complex:

  • components have different temperature profiles with their own MTBF.
  • temperature cycles have to have an impact, at least at the mechanical level.

I am trying to answer this question:

If we average all consumer electronics:

  • does the 10 degrees Celsius rule have any validity
  • or, was it always false / without basis
  • or, was it valid a long time ago but not relevant anymore
  • or, was it based on observations in a specific context
  • or... any other scenario
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    \$\begingroup\$ Does this answer your question? Or is this too complicated? electronics-cooling.com/2017/08/… \$\endgroup\$ – DKNguyen Aug 20 '19 at 20:35
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    \$\begingroup\$ What is it that you were wanting to know about the origin of the rule beyond Arrhenius equation? Is that not the origin? Or do you want to know the origin of that? \$\endgroup\$ – DKNguyen Aug 20 '19 at 20:58
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    \$\begingroup\$ In chemistry, we call it a rule of thumb. It gives a rough guideline, but nothing more. \$\endgroup\$ – Ed V Aug 20 '19 at 22:02
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    \$\begingroup\$ @Thomas The core for semiconductors comes directly from Arrhenius: \$\propto e^{^{-\frac{E_g}{k\,T}}}\$. Silicon's has about \$E_g=1.1\:\text{eV}\$. Use near room temperatures and find the ratio of the reaction rates. You'll see the Arrhenius factor, for example, showing up in the equation for saturation current variation with temperature (see the last factor below): $$I_{\text{SAT}\left(T\right)}=I_{\text{SAT}\left(T_\text{nom}\right)}\cdot\left[\left(\frac{T}{T_\text{nom}}\right)^{3}e^{^{\frac{E_g}{k}\cdot\left(\frac{1}{T_\text{nom}}-\frac{1}{T}\right)}}\right]$$ \$\endgroup\$ – jonk Aug 21 '19 at 4:24
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    \$\begingroup\$ When I design PCBs, I'll compute the total heat that must be removed, and keep in mind the thermal resistor of ONE SQUARE of standard PCB foil ---- 70 degree Centigrade per watt of heat flow. Place the hot components NEAR THE heat-extraction-mounting-bolts. \$\endgroup\$ – analogsystemsrf Aug 21 '19 at 5:54

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