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$\bullet$ An ideal gas at 4.00 atm and 350 $\mathrm{K}$ is permitted to expand adiabatically to 1.50 times its initial volume. Find the final pressure and temperature if the gas is (a) monatomic with $C_{p} / C_{V}=\frac{5}{3},$ (b) diatomic with $C_{p} / C_{V}=\frac{7}{5} .$

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Physics 101 Mechanics

Chapter 15

Thermal Properties of Matter

Temperature and Heat

The First Law of Thermodynamics

The Second Law of Thermodynamics

Hope College

University of Sheffield

McMaster University

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this is Jumper 15. Problem number 60 were given an ideal guess. Up initial pressure off four atmospheres and the initial temperature is 350. Calvin, um, this guess is permitted to expand of you pathetically to its one point type five times of its initial value. So if you call the initial volume beasts of I, then fine was gonna be 1.5 times this initial volume were asked to find the pea final final pressure. Uh, and final temperature of the guests. So grass playing fresher and final temperature of the gas if the, um ratio C p over CV is five over three. If this gas is another attempt, guests. So there couple equations that we need to remember for an independent process. So the initial pressure times the initial volume times gamma being, um, this ratio right equals final pressure times The final volume to power. Gamma. Since we're after final pressure, I divide both of these equations by the final call. You gamma power of it. Right? So these eggs cancel out. So the final pressure's gonna be written. And is the initial believe the final time scam a sedan? We have our equation complained the numbers for him from spheres initial divided by one and half times even shoulders they're gonna cancel out. And his gamble. We have five over three. From here we find out the final pressure to be 2.4 atmospheres. Now, when it comes to the final temperature, we have to remember our outer our our other equation. That goes as, um, initial temperature turns the initial volume. Camel minus one equals final temperature time supplying a ball game a nice one. Now, since we're after final temperature, if you divide both sides by this turn a room and sweet Lizzie isolating the final temperature. Right. Initial times being initial over the final power gamma lines. One initial temperature has given us a scream from over 50 Calvin's and initial volume divided by 15 times the initial volume to the power off five over three minus one. So official volumes they're gonna cancel out we're gonna find out the temperature to the 267 Calvin now in part, a thistles party party we're gonna do, huh? A similar process on Lee. For now, the ratio is gonna be different. That is given to us a spiral over three. This time we're dealing in the bad, Tommy. Guess so. It's gonna be seven over five. But apart from that, we will be using the same explosions. You know, in order to get to our answers. The being these two equations Self party given no CP over. See me to be seven over five. Then the final pressure beaming stole, right. I'm just copying the vision that we had initial pressure stiffer after spears and initial volume. One thing back times initial warrior, am I This time is seven over five. So we find a final pressure to be 2.2. Sad, fabulous fear. Now, the final temperature is the initial temperature Times initial volume finals volume getting minus one initial temperatures. 350 Calvin's, um, tradition volume over looking and for the final on 1.5 times the initial values. So I have been over five like this one, the initials they're gonna cancel of it. So the final temperature is gonna be 298

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