A gas in a cylinder is held at a constant pressure of 1.80 * 10^5...

Question

A gas in a cylinder is held at a constant pressure of 1.80 * 10^5 Pa and is cooled and compressed from 1.70 m^3 to 1.20 m^3. The internal energy of the gas decreases by 1.40 * 10^5 J. (c) Does it matter whether the gas is ideal? Why or why not?

Accepted Answer

Hey everyone in this problem. A sample of gas has its volume reduced. Aisa barrick lee from three liters to one liter inside a vertical cylinder with a movable piston at a pressure of 1.25 atmospheres. The gas temperature decreases by 10 degrees Celsius. And its internal energy by 1000 jewels. Were asked what is the heat exchange queue during the process? If one the gas is ideal and to the gas is not ideal. Alright, So, the first thing we want to think about is what type of process this is. Okay, we're told that this is an isometric process. We hear Aisa barrick process. This means that it has constant pressure. Okay. And we're told what that pressure is. If we have constant pressure, then we know that our work W is equal to the pressure times a change in volume. Alright, so again, isometric process. We think about constant pressure. We have this equation for work. So, we have this information about the work. We're also given information about the internal energy. Okay, We want to find information about the heat exchange Q. So, how can we relate those three things will recall that the change in internal energy DELTA. U. Is equal to the heat exchange Q minus the work W. So, if we want to find the heat exchange queue, we can rearrange and the heat exchange Q. It's going to be equal to the change in internal energy DELTA U. Plus the work W. All right, Delta U. What is this? OK, well, we're told that the internal energy decreases by jewels. So the change in internal energy is going to be negative 1000 jewels. Okay, the energy decreases. So we have a negative value there. Okay, And then our work. Well, we know that this is going to be equal to the pressure times a change in volume. Now we're given the volumes of three liters and one liter. Okay, now we're given the pressure of 1.25 atmospheres. We want to go ahead and convert these to our standard units. So we want the volume and meters tubed and the pressure in pascal's So let's go ahead and do that. Okay, so the volume V one. Okay, the first volume is three liters. Okay, we're reducing from three liters to one liter. So V one is going to be three liters. Okay, now, to convert this to meters cubed, we're gonna divide by 1000. So this is gonna be equal to three divided by m cubed. Which is going to be three times 10 to the negative three meter scooped. And we're gonna do the same thing for me too. Okay, V two is gonna be one leader. We're gonna divide by a 1000 to convert to meters cubed and we get one times 10 to the negative three m cubed. So we have our volumes in meters cubed. Now to do our pressure. Okay, the pressure. We're given is 1.25 MS fears we want to convert this to pascal's So we're gonna multiply our 1.25 by one point 013 - five times to the five Pascal's. Okay. And this is gonna give us 1. times 10 to the five pascal's for our pressure. Okay, So we have our volume and our pressure in our standard unit. Now we can plug those into our equation and work out the answer. So you have negative 1000 jewels plus the pressure 1.267 times 10 to the five pascal's times the change in volume V two, which is one times 10 to the negative three m cubed minus V +13 times 10 to the negative three meters cubed and you'll notice that this quantity, this change in volume is going to be negative and that's because we're reducing the volume, reducing the volume. So the change in volume is going to be negative. So that relates to that reduction and volume of our problem. Okay, so we're going to have negative 1000 jewels minus 253.4 jewels, which is going to give us a final heat exchange of negative 1253.4 jules. Okay, Alright, so we found our heat exchange. Now the question is asking us to find this if the gas is ideal and if the gas is not ideal. And what you'll notice is that we didn't actually use an ideal gas equation to work this out. Okay, we didn't have to assume that the gas was ideal or not ideal in order to figure this out. Okay, so the results are the same. Whether the gas is ideal or not ideal, the heat exchange is still negative 1,253. jewels. Okay, and so we're gonna have answer a That heat exchange negative 1,253.4 jewels for an ideal gas or not ideal gas. Thanks everyone for watching. I hope this video helped see you in the next one.

A gas in a cylinder is held at a constant pressure of 1.80 * 10^5 Pa and is cooled and compressed from 1.70 m^3 to 1.20 m^3. The internal energy of the gas decreases by 1.40 * 10^5 J. (c) Does it matter whether the gas is ideal? Why or why not?

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