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$\bullet$$\bullet$ In the process illustrated by the $p V$ diagram in Figure $15.39,$ the temperature of the ideal gas remains constant at $85^{\circ} \mathrm{C}$ (a) How many moles of gas are involved? (b) What volume does this gas occupy at $a ?$ (c) How much work was done by or on the gas from a to b? (d) By how much did the internal energy of the gas change during this process?

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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

University of Washington

Simon Fraser University

McMaster University

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This is Director 15 Problem number 56. Um, we are giving the PB diagram off I superball process meaning that the temperature is kept at a constant 85 Celsius degrees throughout. This process is we're going from a to B of So in part a were asked how many moves of guests are in votes over Asked what? And iss. So in order to figure out what number moles is for our guests, we need to write down the ideal guess Law PV equals and our tea, right? So, four point B, for instance, we know what the pressure corresponding pressure is and we know what the corresponding volume is. Since we already know what temperature is, we can easily get that information regarding the those that we have to discuss. So let's start by dividing. Lord says off by our times t So these are getting canceled. So the number of miles is gonna be Prince of P V over R t. In this case, if you're right disappoint be the pressure point. B. Tubbs. The helmet probably divided our times. T I'm not quitting the in this year alert the temperature because you go that the temperatures kept costume at all times, so the pressure it be if you read it, it's 0.2 atmospheres, though, right? So let's convert that to Pascual in order to do that, where we're going to do reasonable to fight by wonderfully 013 times 013 10 to 4 or five Paschal's times The volume it point B is pointing one meter. Cute in denominator. I have 8.31 farm juice for Hello, Calvin. And the temperature is and a little convert this Celsius. A defense. Elsie's to Calvin. So I'm adding 273 to it. Right? So then for here what we find number almost 3.681 most. All right, so now in part B were asked what the pressure is and point a Sedale, we are asked. But volume is here. So this is our volume. It point a right. So how we're gonna figure this out since now we know the number of most that we have it right. The ideal guests off for four point A. For instance, it's gonna be Pete A be a equals and our tea. Right? So if you have a sultan's equation for the volume. Then we divide both sides. I the pressure at point a deserving chance allowed what we have here that is played 68681 times, 2.35 years per move. Yeah, really Times the temperatures to 73 plus GT five. Calvin divided by the pressure at point A and Ceci's 0.0.6 atmospheres. We need to convert that two passports, right Them from here we find out the wall in that point A to 0.0.3 three three meter. Cute. So while you is, like, smaller at point eighth and point B, I know in part, See were asked how much work done is we go from A to B. How much work dub, right? So again, let's remember that this is the last of thermal process. So for I said terrible process The work is given by and r a t l. As we've five of Valium divided by a vicious volume for our case, the liver of A to be so our firewall, You would be of all of that point be an initial long believed to be the volume that point a so we could rewrite our treasure. Such is this right. So we need to do is to plug in the numbers 48 681 most times are is a 0.35 jewels. Permal Calvin times the temperature is to 73. Philosophy t help it is. We have l end off the ratio. The ball leave it toward be was point. What meter cubed. We calculated the volume that point of a to be 0.333 meter cubed. So if you calculate the work done is going to be 2230 Jules again. Please pay attention to the fact that the work it's positive, Which means this work is done by the gas right work Is Doug by the gas now in party for asked to calculate to change in internal energy through this process again. Please remember that this is a vice of terrible process. And for isil federal processes, we have the change in eternal energy to be zero uh, please read the related portion or your textbook. Uh, but if we were to explain it in a straightforward way, the change of internal energy is number. Will most hers TV tons, Delta teeth in for our case, the temperature is constant, which means Delta T equals zero. So then, if doubt that equal zero, so is doubt you. Which means he durable energy is constant for this princess.

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