Hi, guys. I'm doing problem 21 from chapter 18 and it tells us that a mon atomic ideal gas is undergoing nicer thermal expansion. And it it gives us a little diagram and says what is the temperature of the beginning and at the end of this process, and then asks how much work is done by the gas during this expansion? Okay, so if we're dealing with and a nice of thermal expansion, um, of an ideal gas, So an ideal gas always should satisfy the ideal gas equation. P vehicles on our tea, right? PV equals on Artie. Okay, so now, looking at the diagram, we're just just showing, um, just showing an ice, a thermal expansion. You can read all from the diagram, either at the end point or uh either at one end point or the other or somewhere in between. If you can actually see what exact value it's hitting, you can read off the pressure in volume. Okay. And since this is the nicest, their p times, he should always be the same. So shouldn't matter where you take it. But, um, no matter where you you do, it should get the same answer for tea because it's nicer. So that means that the temperature should be the same the whole way through, uh, holy through the curve. And so you can rearrange the vehicles, Artie, to get t equals P V over nr and then calculating that calculating this you get about 408 Kelvin. So you have to be a little bit careful here because the pressure on the ah in the diagram is given Killa Pascal's right. So, um, what you may accidentally think is 400 Pascal's actually 400,000 Pascal's maybe a little bit careful about that, and you get so 408 Kelvin, if you do things correctly and then, uh, let's part a soap for part B and es with work done and the work done for a nicer thermal expansion and Artie Timesthe log VF over v I. So this is kind of nice to memorize, but if you don't have this memorized, you can actually get it from ah. Using work is the interval of P. D. V and then replacing P with and our tea over v using the ideal gas equation. Cuticles are dirty and then you can you can get to this fairly easily. Um, but anyway, this is This is what you need for the second part and do this calculation, you'll find it's about 555 killer Jules here. So end and were given in the problem are is a constant T is what we got from part part A 408 Kelvin's lefties. That and then VF and the initial are also given the problem. And so we find our final answer. 555 killed, Jules.