# Differential symbols

1. Apr 6, 2006

### ak416

What do the following differential symbols mean: δ, đ (the line is actually more slanted)

Ive seen these come up in my thermal physics class. For example δU or đW. Is the little delta equivalent to writing the uppercase "triangle" delta? Also i think the d with the line has something to do with dependence on direction. Am i right?

2. Apr 6, 2006

### TD

It has to do with being a 'total differential' (such as dU) or not (such as q and w in dU = dq + dw) which is why a strikethrough is sometimes used for the d of dw and dq, to emphasize that those are not total (or exact) differentials. A total differential is path-independant, the others aren't.

3. Apr 6, 2006

### arildno

In thermodynamics, that notation typically means that you haven't got an exact differential.

4. Apr 6, 2006

### ak416

Well i know when writing an equation such as dU, we must write: dU = ∂U/∂Q *dQ + ∂U/∂W *dW . But in this case What's W and Q. If they call dW "Work done on system" and dQ "Heat added to system" Then i guess its meaningless to call W something right? And if dQ = T*dS I guess we can call Q = TS ? Sorry if this is getting off the "math" topic but if anyone can answer this physical question it will help also. But as for the math, is there any connection between what I said and what you call a non exact differential? Like what do you mean path independent? Heat and Work can only move in one dimension (they're scalars)...

5. Apr 6, 2006

### ak416

or by path dependent you mean that dQ and dW depend on eachother and you cant keep one constant without changing the other?

6. Apr 7, 2006

### TD

I'll give a physical 'story' to show the difference between path dependence and independence. Say you're climbing a mountain and you're going from place A (at 100m heigth) to place B (at 600m heigth). The overall altidude difference you'll have accomplished is path-independent. It doesn't matter which 'road' (=> path) you use to go from A to B, you'll always have risen 500m. The distance you've travelled is path-dependen however! You can take the shortest way from A to B or you could 'go arround the mountain' using a twisty road instead, but you'll have done a lot more kilometers

Now back to thermodynamics: the interal energy is path-independent (and thus an exact differential). It doesn't matter which 'path' a system follows to go from situation A to situation B, the net change in interal energy will be constant. The work done however, is path-dependent (and thus not an exact differential) since you can achieve the change in situation in many manners, not all requiring the same ammount of work to do.

Thermodynamics has been a while for me, I hope I didn't say anything stupid here and that it's a bit clear to you now