Hey, everyone. So by now, we've studied the ideal gas law and the first law of thermodynamics, which, remember, relates variables like heat and work when you have a system or a gas that's changing from one state to another. Now in some problems, these changes will only be described in the text of the problem. But in others, you'll have to take these changes and you'll have to map them out or draw them in what's called a PV diagram. So in this video, I'm going to introduce you to what these PV diagrams are. They're going to be really useful for the rest of thermodynamics, so it's really important that you learn them very well. And I'll also show you how to calculate the work that's done by a system using these diagrams. So let's go ahead and check this out here. Basically, what a PV diagram does is it plots pressure, that's the p on the y-axis, versus volume, that's the v on the x-axis. We have p and v. And basically what these processes do or these diagrams do is they graph these things called thermodynamic processes. And this is just when any system or gas changes between a state. So let's just dive right into our first problem here. So we have that a gas is expanding from a volume of 2 to 5 at a constant pressure. That's a thermodynamic process. The whole idea here is that now we're going to take this text and this picture and we're actually going to draw it out on this graph. Now even though it's a graph, a lot of textbooks will refer to this as a PV diagram so that's just what we're going to call it. So let's get started here. We're going to draw this out on our PV diagram. So we have a constant pressure of 100 that's right here. And then what we have here is we're going to we have, we're going from 2 meters cubed, so that's sort of like our initial point right here, and then we're going to go to 5 meters cubed. So that's going to be right here. So the process will actually just look like a straight line that connects initial to final because it's a constant pressure. So what happens is this 100 here will never change. So that's really what this process looks like. Notice how we indicated this arrow here because we're going from initial to final. That arrow is going to be super important. That's the first part. Now let's jump into the second part here. We're going to calculate the work that's done by the gas. So that's just the equation w by. Now remember, if we have constant pressure, we can use this equation p times Δv. Now do we have constant pressure here? We do because we're told that in the problem. So we can totally use this equation here. So the constant pressure is going to be 100, and the change in volume is just going to be from 2 to 5. So this Δv here is just going to be 3. Right? So this is going to be 3 and you work this out and you're going to get 300 joules. Pretty straightforward. That's just the work done pΔv. Alright. So now let's jump into part c here, which is we want to calculate the area under the path of this process. What does that mean? Well, the path just goes from initial to final. The area underneath that path is just going to be this rectangle right here. So all we have to do to calculate the area is just calculate the area of a rectangle. Right? That's just base times height. So the base of this rectangle here goes from 2 to 5, so it's just 3. The height of this rectangle is 100. And so therefore, if you do 3 times 100, hopefully, you guys realize that you should get 300 joules. Notice how these two numbers are the same, and that's no coincidence here. So what it so the thing I want you to know here is that the work that is done in any thermodynamic process, no matter what it is, is always equal to the area under the curve. So this should make some sense to you over this process because if you think about it, what happens is the base really i
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PV Diagrams & Work: Study with Video Lessons, Practice Problems & Examples
PV diagrams plot pressure (P) against volume (V) to visualize thermodynamic processes. For constant pressure, work done (W) can be calculated using the equation
Work and PV Diagrams
Video transcript
Finding Value of V on Axis
Video transcript
Hey, guys. So I hopefully got a chance to look at this problem here. This one's kind of interesting. So what we have in this problem is we're given this thermodynamic process, and we're told what the work done is. It's
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What is a PV diagram and how is it used in thermodynamics?
A PV diagram is a graphical representation that plots pressure (P) on the y-axis against volume (V) on the x-axis. It is used in thermodynamics to visualize the changes in a system, particularly gases, as they undergo various processes. These diagrams help in understanding how pressure and volume change during processes like expansion and compression. By analyzing the area under the curve in a PV diagram, one can calculate the work done by or on the system. For instance, the work done during a constant pressure process can be calculated using the equation
How do you calculate work done in a PV diagram for a constant pressure process?
To calculate the work done in a PV diagram for a constant pressure process, you can use the equation
What does the area under the curve in a PV diagram represent?
The area under the curve in a PV diagram represents the work done by or on the system during a thermodynamic process. For a constant pressure process, this area is a rectangle, and the work done can be calculated using the equation
How do you determine the direction of a process on a PV diagram?
The direction of a process on a PV diagram is indicated by arrows that show the transition from the initial to the final state. This is crucial because the direction affects the sign of the work done. If the process moves from left to right, it indicates expansion, and the work done is positive. Conversely, if the process moves from right to left, it indicates compression, and the work done is negative. Always ensure to mark the direction with arrows to avoid errors in calculations.
Can you use the equation W = PΔV for processes with changing pressure?
No, the equation
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