Start typing, then use the up and down arrows to select an option from the list.

Hey guys, so 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 giving this thermodynamic process here, and we're told what the work done is, it's two times 10 to the fifth. And what we wanna do is we want to figure out the value of V. One indicator on the axis. So really, what we're trying to find here is we have some kind of a thermodynamic process. It changes from this pressure to this pressure. But what we wanna do is we want to figure out what is the volume, basically, what do the tick marks represent on RV access? That's kind of what we're interested in. So let's go ahead and check this out here. If we're given this thermodynamic process and we're asked to find something about the work that's done, we're gonna start off with our work equation. Now, what we can't do in this problem is we can't use p times delta V because the pressure does not remain constant. Remember, we can only use p delta v and we have flat processes, but this one goes up like this, so the pressure is changing, we can't use it. So instead we're going to have to do is relate the work done to the area that's under the curve or under the process. So what's happening here is that we have this process that goes from here to here, and really the work that's done, It's going to be the area that's under this shape right here. So this w is equal to two times 10 to the fifth, and we're gonna have to do is we're going to have to relate this work to one of the area equations that we have for shapes like a rectangle or triangle or trapezoid, or whatever. So what happens here is if we look through this shape, this kind of looks like a trapezoid, right? So we have here in the trapezoid is I'm gonna call this base one, This is gonna be base two, and then this is gonna be my height of my trapezoid, right? The trapezoid doesn't always have to look like, like this, like the shape here, because you could have this as being as as a trapezoid as well. So, here's what's going on, we're gonna use the area for a trapezoid, which is going to be one half, this is gonna be base one plus base two times the height. Now we're told here, is that this is equal to two times 10 to the fifth. So what is base 1? Base to? What does height? What does all that stuff? I mean in terms of the variables that we have here. So what's going on here? Is that this base one represents one times 10 to the fifth. This base to represents three times 10 to the fifth. So what I'm gonna do here is I'm gonna replace this with one, half, one times 10 to the 5th, Plus three times 10 to the 5th, and then times the heights. Well, what is this height here? Well, if you look at this at this graph, the height is going to be the difference between this piece and this piece or this part of this part here on the V axis. So the height here of my trapezoid actually represents the difference between V one and three times V one. So the height here is actually gonna be two times V one, right, we're going one and then two of whatever unit that is. So that's sort of gonna be my uh my height here, it's gonna be two times V one, so this is going to equal two times to the fifth. So now what I can do here is all I have to do is solve for this V one. Okay, so here's what's going on, we're gonna have, I'm just going to combine these two things in this parentheses here. So we've got is four times 10 to the fifth Times two. V 1 is equal to two times 10 to the 5th. And so now we're gonna do is one half of four times 10 to the fifth is just gonna be two times 10 to the fifth. So two times to the fifth times to be one equals two times 10 to the fifth. So what happens here is we can divide out This two times 10 to the 5th from both sides. And what happens is this goes away and this just becomes one. So we've got two V one is equal to just one, right? And so therefore the V one is equal to 0.5 m cubed. So that's basically what the first little tick mark represents. So what's going on here is this is 0.5, this is one And this is 1.5 m cubed on the x axis. And so what happens is if you go ahead through and double check real quick if you basically just go ahead and plug these numbers back into this trapezoid equation, which you'll get here is two times 10 to the fifth. Alright, so that's over this one. Let me know if you have any questions.

Related Videos

Related Practice

© 1996–2023 Pearson All rights reserved.