Mountains are always used as the example of a state function, viz., altitude. It matters not from your final altitude's point of view if you climbed that central Grand Teton by starting at the left and tramping over Nez Perce then over Middle Teton arriving at last on top of Grand Teton or you climbed a leisurely trail of cutbacks up Grand Teton to start with. When you're on the top, you're on the top, and your altitude, having suffered ups and downs in the first instance and steady rises in the second, is still that of the top of Grand Teton. Having tramped around the Texas State Fair several times during its final weekend, I do have a preference in climbing Grand Teton. Of course, when we think about that expression, it's clear that average energy will change if either the populations, i , change or the energy levels themselves, i , change.
Work comes in a multitude of flavors.
So gravity is a collapsing force. Raindrops are spheres in the absence of wind shear. We'll look into the causes of surface tension later in the semester, but you know from previous courses that the van der Waals attraction between liquid molecules works equally in all directions on a molecule in the bulk, but only on the bulk side of a surface molecule. Finally we can come all the way up to 3-d, in which we imagine volumes changing against opposing pressures. Actually the differences here can best be remembered by thinking of a soap bubble.