# Is work path or state function, or both?

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#### m25

##### Full Member
7+ Year Member
So the equation for work is:

W=Fd

in which d is the displacement of the object. So for example if, you raise a box 1 meter and then lower it 1 meter, work is zero since the displacement is also zero.

But I also keep hearing how work is a path function, and came across this idea on the internet that work is only a state function when under the influence of a conservative force field, such as gravity, and work is a path function otherwise.

So taking this into consideration, the work done by the gravity to raise a box 1 meter and then lower 1 meter is zero, but is work done by ME to raise a box 1 meter and then lower 1 meter also zero?

Also, are there any other conservative force fields that we will see on the MCAT? If so, what are they? For example, would electric fields also conservative??

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Work itself is a path dependent function. The change in energy is path independent (i.e., state function). I know it's weird, but think of it this way:

If I want to calculate the Work done, I have two options:
1. I can use the work equation, making sure to use the parallel force that was applied across a displaced space
2. If there is no heat exchange (q), I can look at the starting and end point, and see what the energy difference is. Since the change in energy of a system can only be done through Work or heat - and there's no heat - the difference will correspond to Work.

Work is path dependent.

Let's say you want to go from NYC to LA. You can take a straight path or you can zigzag. If you zigzag, the work will be more. At the end, however, you end up in the same place.