Arrhenius Model – believe it or not you use it all the time..and So does Martha Stewart!

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Adam Bahret

Let’s discuss the Arrhenius model.  One thing you didn’t know about is that you may already be an expert in it.  How could that be you ask? You have probably used it many times at home.

You use the Arrhenius model to accelerate and decelerate food decomposition everyday, cooking and refrigeration. When you slowly cook food in a pan you are accelerating it’s interaction with oxygen. You are effectively spoiling it as if it was left out on the counter in a controlled and accelerated fashion. Ever notice how rotten onions smell sweet?…a lot like slowly cooked, caramelized, onions? It’s the same process but you accelerated the onion aging with heat. Well how about those onions you don’t want to use yet? You put them in the fridge where they are cooled down so that the aging slows until you choose to take it out and accelerate it to a perfect sweetness in a frying pan. Ok now I’m hungry, hold on. Ok I’m back.

Arrhenius onion cookingHaving done that process qualifies you as an experienced reliability engineer. You likely have even wrote out the acceleration equation; Set the fridge at 45F to slow down a weeks for aging to two months and put the stove on 350F to accelerate two weeks of aging into 20 minutes.

“But hey Adam, I get all this fun cooking stuff but there is no way I’m going to understand the complex equations behind hit.” “Well Sir/Ma’am you are absolutely wrong.” The equations are as easy as making Ramen Noodles. Here is the base principle that pulls it all together. If you look at the Arrhenius equation there is one factor in there that turns many people away from using it because it has to be selected and it is very mysterious. It’s the activation energy. So what is the activation energy?

The Arrhenius model is an accelerated life model based on the assumption that the products primary wear-out mode is driven by chemical reaction. Some examples of this are plastics or rubbers breaking down, materials interacting to form new materials, loss of material through evaporation and oxidation. Greases and oils loosing their lubrication properties from material break down.

In an Arrhenius based acceleration model the test temperature is set at a static level that is above the normal operating temperature. Using an interpretive equation the products wear-out failure time at this higher temp can then be translated to life at the normal operating temperature. It’s that simple, well not exactly, it takes a little finesse to get the interactive acceleration factor correct for the specific material.

Broken Eggs

The activation energy has a simple analogy.  If you take two eggs and roll them into each other one of two things will happen. They will either bounce off of each other and go off in a new direction or break and mix. What dictates which outcome occurs? How fast they were rolling when they hit. There is a specific speed that will dictate which outcome occurs. This speed translates into a specific amount of energy that is enough to break the shells. The name for this energy threshold is “Activation energy”. If they hit with less than the activation energy they just bounce off of each other. If it is more then they break and mix.

Now if the moving items are joined molecules instead of eggs the “breaking” when the impact is above the activation energy for that material i it breaking it’s internal bonds and joining bonds with the other molecules.  A chemical reaction has occurred. So the faster you get a molecules moving in random directions the more collisions you will have above the threshold activation energy. The average speed the population is moving is a direct correlation of temperature.

  • Higher temp
  • Harder and more frequent impacts
  • More chemical reactions between materials
  • Faster aging!


Do these look burnt to you?  I should do this in a temperature chamber!

IMG_0531Here is the equation behind that recipe line in your cookbook “Simmer at 200F for 20 minutes”

In exponential form, the effect of temperature on reaction rates using the Arrhenius equation becomes:


k – is the rate coefficient,

A – is a constant characteristic of the reaction,

Ea – is the activation energy,

R – is the universal gas constant

T – is the temperature (in degrees Kelvin).


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