# Thermodynamics and heavy use of partial derivatives

1. Dec 2, 2013

### Woopydalan

Hello,

I am not completely certain why in thermodynamics, it seems that everything is done as a partial derivative, and I am wondering why? My guess is because it seems like variables are always being held constant when taking derivatives of certain things, but it is still somewhat a mystery to me.

Also, I noticed since starting my chemical engineering class, a lot of things are approximated, it seems like there aren't a lot of closed form solutions to thermodynamic problems and numerical methods must be used.

Last edited: Dec 2, 2013
2. Dec 2, 2013

### SteamKing

Staff Emeritus
In thermo, in order to completely define the state of a substance, it usually takes more than one property (like pressure, temperature, specific volume,etc.) to do so. When you want to find out what happens during a change of state, for example, then you vary one property while keeping the others constant, which is what partial derivatives are designed to do. It's unclear why this should be a mystery; after all, these concepts should have been covered in your calculus courses already.

3. Dec 2, 2013

### WannabeNewton

I had a professor who said that thermodynamics is the theory of partial derivatives ;)

But I agree with SteamKing that there is no deep reason for the dissemination of partial derivatives throughout thermodynamics. It is one of the most predominant tools of calculation and theory in thermodynamics because of the reasons given by SteamKing. You will notice in physics that different physical theories make heavy and frequent use of very specific things from math. Electrodynamics does this with vector calculus, general relativity does this with tensor calculus and so on.

As far as approximations go, this isn't specific to thermodynamics. Approximations are (rightfully) used heavily throughout physics and for obvious reasons.

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