CALC The temperature of 0.150 mol of an ideal gas is held constant at 77.0°C while its volume is reduced to 25.0% of its initial volume. The initial pressure of the gas is 1.25 atm. (c) Does the gas exchange heat with its surroundings? If so, how much? Does the gas absorb or liberate heat?

Video transcript

Hey everyone in this problem, we have 0.84 moles of an ideal gas with an initial pressure of 1.6 atmospheres. And it's taken through an ice a thermal process at 82°C? The volume is lowered to 40% of the original volume. And were asked does heat flow between the gas and the surrounding occur? Okay. And if yes. How much and in which direction? Okay. And we're told that the positive sign is going to indicate that it's into the gas and the negative will indicate out of the gas. Alright, So, with a problem like this, let's start with what type of process we have. That's gonna dictate what kind of equations we use. Um And what kind of information we know. So, this is an ice a thermal process. And we're told in the problem ice a thermal Okay. And in an icy thermal process, what we get is we get a constant temperature. Okay. So the temperature of 82°C that we're given is going to be constant throughout the process. Okay. And because we have this constant temperature that delta U. The change in internal energy, It's going to be equal to zero. Now, if the change in internal energy U. Is equal to zero, what that tells us, is that Q. The heat is equal to w the work. Okay. Alright. So, cue the heat. Well, that's what we want to find. We want to find whether heat flows. So we want to find information about Q. Okay. So now that we know that Q is equal to w Because of the ice thermal process, we can also find W. Instead of finding Q. Okay. All right, So what about w How do we calculate W in an ice at their own process? Will recall that we can write W. Is equal to end R. T. Lawn of the ratio of the volumes. V. Two over V. One. Now. And is given in the problem. The number of moles are as a gas constant. T The temperature were given in the problem and these volumes well were not given the exact value of the volumes but we are given a relationship between the initial and final volume. So let's go ahead and use that information we know and see where we can get. Okay. And again, we're gonna find W the work but we know that that's equal to the heat Q. Because of our ice. A thermal process. So we get n number of moles 0. Times are the gas constant, which is 8.314. And the unit here is Jules for Mole Calvin. Many times the temperature too. We have 82°C. And then we're gonna add 273.15 to convert this to Calvin. Okay. And then we have times lawn. Of what? Well avi to What information are we given about V two? We're told that the volume is lowered to 40% of the original. Okay, So V two is going to be 40% of U. One. Okay, so we're gonna have V2 is 0.4 times v one Divided by View one. Now we can divide by the V. One. Okay. We're gonna be left with just a number inside of the lawn that we can evaluate. Okay. So because we're looking at the ratio of the volumes, we didn't need to know the exact volume. V. One or V two. We just needed to have the relationship between the two. Alright, we see here we have a mole and Calvin K times per mole kelvin. So those units will cancel and we'll be left with units of jewels which is what we want for work. And so we have the right units here. Okay. And this is going to be 0.282364 jewels. K. Times lawn. And again, the view, once we can divide we get lawn of 0.4, This is going to give us negative 2,272. jewels. And that's our work. W now we're trying to find information about heat because of the ice to thermal process. We have this relationship that Q. Is equal to w So this means that Q is equal to negative 2272. jules. Okay. Alright, so we figured out that there is heat flow between the gas and the surrounding. Okay, we have the amount of 2,272.66 jewels, and we have a negative and the negative indicates that the heat is flowing out of the gas. Okay. And so our answer, if we take to the closest We get f. Or sorry, we have the negative a negative 2270 jewels and it's flowing out of the gas. Thanks everyone for watching. I hope this video helped see you in the next one.