Path Independence and Heat

A path independent property is one that is the same no matter how it is determined. That makes very little sense so let’s try to use a simple example to explain it.

Imagine that you are riding on a roller coaster. If we determine your potential energy at the top of the first hill and then later when you are lying, face-down, on the ground at the bottom of that hill, your change in potential energy would be the same whether you leapt out of the car and fell (a very bad choice) or if you rode the entire ride, got out of the car and then walked to the bottom of the hill and lay down (a much safer choice). So, in this example, the change in potential energy is path independent—that is, it does not depend on the path you took from one spot to another.

On the other hand, your kinetic energy when you first reach the ground is tremendously path dependent, since if you fall you will be moving very quickly when you reach the ground, while if you walk you will be hardly moving at all.

It turns out that heat is almost always path independent. In fact the only time it isn’t path independent is when electricity is involved (for instance inside a battery) or when the pressure is changing during the reaction. Since we do most of chemistry in open containers, the pressure is essentially constant and we only deal with electricity during one small segment of chemistry (called electrochemistry) we can treat heat as if it is always path independent.

We care about the path independence of heat, because it is the basis of Hess’ Law.

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