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Rutgers, The State University of New Jersey

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welcome to our third example video. Looking at the first law of thermodynamics in this video we're going to consider an is a thermal process according to what we see here on our plot. And the question is, at what temperature does this occur? And also how much work is done over the course of this process? Now the technically, we don't need to answer the first in order to answer the second. Remember that for work done, it's pointed to the right, so it's going to be positive. It could be the calculated, his NRT natural log of V two over V one. Or it could be calculated as work equal to P V Times natural log of the two over the one. Either one will work. And remember, PNV can be picked at any point so we could use when we're at six times 10 to the five past gals and two leaders, or at one times 10 to the five Killer Pascal's, our past cows and 12 leaders. So, uh, and you can calculate it either way. Probably easiest to do it this way, in which case you could say work is equal to We'll start with the initial condition six times 10 to the five Pascal's multiplied by volume, which is two leaders. That two leaders is going to be too divided by 1000 cubic meters, multiplied by the natural log. We have 12 leaders over two leaders. We don't need to worry about the units here because any adjustment we make would just cancel out in the division and the ratio here. So it's the ratio that matters so and this would be the work done now to calculate temperature, we can use the ideal gas law PV equals N R T. So t is going to be equal to P V over N r. And again we can use any set of PV that we want. We could use the first one just to be consistent. So T is going to end up being equal to six times 10 to the five past gals multiplied by a volume of two leaders. That's two divided by 1000 cubic meters, all divided by n times are now. In order to do this one, we're going to need to calculate the end. Remember, the N is equal to the total mass. We have 20 g of argon, so that zero point 0 to 0 kg divided by the Mueller Mass. Which is going to be 0.4 kilograms per mole. So once we do this calculation, which comes out to one half moles approximately, we have 0.5 moles multiplied by 8.31 Jules per mole Kelvin, which is our gas constant. Okay, and that's all we need. In order to calculate our temperature and our work notice, you could try the other position at one times 10 to 5 Pascal's and 12 leaders. You'll get the same results.

University of North Carolina at Chapel Hill