PV-diagrams and expansion work. What are PV diagrams? Work done by isothermic process. Carnot cycle and Carnot engine. Volume ratios in a Carnot cycle. S or entropy is a valid state variable. Thermodynamic entropy definition clarification.
Reconciling thermodynamic and state definitions of entropy. Efficiency of a Carnot engine. Proving that it is the most efficient. Video transcript In the last video, we saw that a system could do work by expanding. And in the situation we drew, we had a situation where the ceiling was movable. We had this piston and we, like in our process video, we had a bunch of pebbles.
We removed a pebble, so the pressure in our system, if we assume that it was just so small that the pressure was constant, it pushed up on the piston with some force. We figured out that that force, since pressure is force per area, we just multiplied pressure times the area of our piston, and we got the amount of force we're applying. We apply that, and then we multiply that times the distance that we push the piston up, and then we get the amount of work that it did by expansion, or the expansion work.
We said, well, you know we could have rewritten that. If you said pressure times our area, times our distance, we could instead write that as pressure, times the area, times the distance.
And the area times the distance is the change in volume. And so we came up with a neat little formulation, that the work done by a system could be written as the pressure times the change in volume. So in this case, I wrote the internal energy formula, where it's the work done by the system. So I did a minus, right? Because when you do work, you are giving energy away to someone else. So in that situation, we did a minus. And so instead of writing work, we could say, minus the pressure, times the change in volume.
And remember this is a quasi-static process. And we're doing it at very small increments. We're assuming that this change in volume is very small, and that the pressure is roughly constant while we're doing this. And of course that's not the case, right? If we did this, if this was a large change in volume, or if this happened all of a sudden, if these were really big pebbles, then our pressure will change as we expand. So it's hard to say what the pressure times the change in volume is. But if we assume things are really, really being done in very, very small increments, we could say, OK, let's say the pressure was constant over that small increment, and then we can multiply it by the change in volume.
Now let's see how this can relate to some of what we've done before with the PV-diagram. And so far, all we've seen the PV-diagram, or what I used it for, is to kind of help explain the difference between quasi-static processes, or to say when macrostates are defined. But let me now do something more useful with it.
And this will give you an idea, or start giving you an idea of why people who study thermodynamics love these so much. So before I did anything, when my canister was just here, I had all the pebbles on it. And we were in a state of equilibrium. I could describe all of its macrostates, its pressure, its volume, its temperature. I could describe its internal energy as well. So let me draw it here. So let's say I was at this state.
This was state number 1. State number 1 was right there. And then, let's say I just start removing pebbles. Remember, if I just remove all the pebbles at once, the system's going to go into flux. We wouldn't be doing a quasi-static process, or a reversible process, which isn't always the same thing. But for our purposes, we wouldn't be in equilibrium the whole time.
And we would have to wait to get to equilibrium. And at some point we'd have some pressure and volume that's down here. This is if we weren't doing it as a quasi-static process. Now we are, what I showed in the last video, we are doing it as a, or we're trying to get close to a quasi-static process, because we're doing it in small increments, with these little pebbles. And if these aren't small enough for you, you could do it in smaller pebbles. So we're moving incrementally. So, for example, in that last video, we maybe moved from there.
We removed one pebble and we got right there. You remove another pebble and you go right there. And the benefit of doing these quasi-static processes is you really get a path going from one state to the next. Let's say when you remove all but one of the pebbles, just, you know, this describes our path. So let's say we are in state 2 and we've removed all but one. Let me draw that. So state 2 will look something like this. I'll draw it really quick. So that's our container. We only have one pebble left on top. And then of course we have the gas now.
Let me write this down. This is state 2. And most importantly, we all work towards a better future for not only ourselves and our company, but for the collective whole of our community. As the fastest growing media brand in our market, our portfolio currently includes:. Volume One, a twice-monthly paper packed with feature stories, special sections, and the most robust event listings found anywhere in our market. Volume One's sister publication - a complete print, online, and social guide for local events, listings, stories, and perspectives, all delivered through a family-oriented lens that explores themes including community, discovery, creativity, activity, living, and more.
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