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There is one thing (among others) that plague me and that is the whole concept of work. It keeps popping up as a common denominator.

In the context of thermodynamics, the internal energy is the measure of the sum of kinetic energy and the potential energy.

The change in internal energy from state i(initial) to f(final) gives Q(heat) + W(work).

What I am really confused about is working being the negative of the product of pressure and change in volume.

W = -PΔV

I see this in mechanics and as well as in electricity but my understanding of them as regard the NEGATIVE sign continues to be fuzzy.

Let's start with an example:

Suppose I have a cylinder heated (in contact) with a thermal reservoir. At state i, the piston is height Li from the base of the cylinder. At state f. the piston has height Lf from the base of the cylinder.

Li < Lf

Essentially, the piston is being pushed outward as the cylinder is being heated.

Now,

W = -PΔV

As the piston is being pushed outward, the change in v is positive because Lf>Li and pressure decreases and therefore pf < pi and so pressure is negative.

Therefore, in this example, W = -PΔV.

Is my understanding flawed?

If it isn't then would it be correct to state that if the pressure does not change (assuming a certain pressure could be maintained within the system as), then W = PΔV?

work done by the system = negative W

work done on the system = positive W

heat supplied to the system = positive Q

heat supplied from the system = negative Q