Would someone please elaborate on Path Function?

[Ultimeaciax]

I don't understand how Heat and Work are path functions. How are they dependent on the path? Say work, the amount of work I get done is proportional to the distance taken. So, does it really matter how I take the path? No matter what path was taken, I still do the same amount of work. Though the distance and force may be different.

So far, this is what I gathered for my note and it still doesn't make any sense to me why heat and work are path functions

PATH FUNCTIONS - describes the transition/path of a system from initial to final state. Ex: Work, Heat, Length

Constant Volume (Isochoric): if ΔV = 0, then work = 0 → ΔU = q + w → ΔU = q → thus heat (q) may change

Constant Pressure (Isobaric): if P = constant, then V still able to change → work is also changed → ΔU = q + w

Constant Temperature (Isothermal): if T = constant, then ΔT = 0

Insight to this is greatly appreciated.

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[pm1]

I don't understand how Heat and Work are path functions. How are they dependent on the path? Say work, the amount of work I get done is proportional to the distance taken. So, does it really matter how I take the path? No matter what path was taken, I still do the same amount of work. Though the distance and force may be different.

So far, this is what I gathered for my note and it still doesn't make any sense to me why heat and work are path functions

PATH FUNCTIONS - describes the transition/path of a system from initial to final state. Ex: Work, Heat, Length

Constant Volume (Isochoric): if ΔV = 0, then work = 0 → ΔU = q + w → ΔU = q → thus heat (q) may change

Constant Pressure (Isobaric): if P = constant, then V still able to change → work is also changed → ΔU = q + w

Constant Temperature (Isothermal): if T = constant, then ΔT = 0

Insight to this is greatly appreciated.

Work is a path function because W = F x d. Depending on the path you take, work will change.
Even if you are going to the same end point if you take a shorter path d will be smaller, hence W will also be smaller. While if you choose to take a longer path, d will be bigger, Work will also be bigger. Thus, the way you move from one place to the other determines your work.

 

[milski]

Careful. d in the formula quoted is displacement, not distance. For conservative forces, like gravity, the work done will depend only on the initial and the final position and will not be a path function. Only for non-conservative forces, like friction, will the work depend on the path taken. That should make sense, since for friction the force is always in the opposite direction of the force - no matter in which direction you're moving, the amount of work done increases. For a conservative force, the direction of the force and the displacement are not related, so moving in one direction "cancels out" the work done by moving in the opposite direction.

The question seems to be more about work/heat from thermodynamics perspective. The way to approach this is to start with ΔU=W+Q. This tells you that any changes done to the internal energy of the system are sum of the work done and the heat transferred. The internal energy itself is a state function - for a given state you know the precise internal energy. If you want to move the system from state A to state B, you want to change its internal energy by ΔU.

Since ΔU=W+Q, there is an infinite number of combinations of W and Q which lead to the same ΔU. You can do more work and less heat transfer, or more heat transfer and less work, etc. That multitude of choices is what makes work and heat path function - just by knowing the initial and the final state you don't know the path that was taken to get there. The same way just by giving you the number 5 you don't know if it was found as the sum of 4+1 or 2+3.