Two moles of an ideal gas are heated at constant pressure from T = 27°C to T = 107°C. (b) Calculate the work done by the gas

Video transcript

Hey everyone, welcome back in this problem. We have a container filled with 1.8 moles of an ideal gas. Were asked how much work is done by the gas as it's heated from 10°C to 110°C while keeping the pressure constant. Okay. All right. So we want to find some information about the work. We're told that this is a constant pressure process. Okay, This means that we're talking about an ice of eric process. We were asked to find work. Let's recall. If we have a constant pressure process, we can write the work w is equal to the pressure P times of change in volume. V two minus V one. Okay, so we want to calculate work but looking at this equation well, we need the pressure and we need both the initial and final volume and we don't have any of that information. Okay, what we do know is information about temperature and information about and the number of moles. Okay, we also know that this is an ideal gas. So let's recall how we can relate pressure, volume and temperature and the number of moles with an ideal gas. We have the ideal gas law, ideal gas law which states that PV is equal to N R. T. Okay, no, We have both the initial and final stages or states. Okay, so let's write the ideal gas law for each. We have P- one. V one is equal to N R. T one And we have P two. V 2 is equal to NRT two. Well, we know that this is a constant pressure problem. So P one and P two are going to be equal. Okay we'll just call it p the pressure, the same pressure through. So we get P V one is equal to n R. T. One and we get P V two is equal to n R. T. Two. All right, well, how can we relate this to this equation for work that we know the equation for work? We have P times V two minus V one. Let's go ahead and call this equation one on the left hand side. An equation two on the right hand side. It will notice that if we take equation two and subtract equation one and the left hand side is going to give us this expression we have for work. Okay? So let's do that. Let's take equation too. And subtract equation one. Okay, so we have PV two equals n R. T two and we're going to subtract P V one is equal to n R. T. One. Okay, On the left hand side we're gonna get PV two minus PV one equals on the right hand side N R T two minus N R. T one. If we go ahead and factor we'll find as we get P V two minus V one on the left hand side and n R times T two minus T one on the right hand side. Okay well look what we have here. Okay this PV two minus V one is equal to the work. Okay. In this expression that we found earlier. So what that means is we can write the left hand side of this expression as the work. W. So now we have the work W. Is equal to N R. T two minus T. One. Okay, so using the ideal gas law we were able to write an expression for the work in terms of the temperature instead of in terms of being or sorry, in terms of the pressure and the volume. Okay, now we're given information about the temperature in the problem. So we can go ahead and plug in the information we know to find that work. W let's give ourselves some more room to write here Now and there's a number of moles in the problem. We're told that we have 1.8 moles, 1.8 mol Ours our gas constant which is 8.314. And the unit is jules from old Calvin. Can you can look that up on the table in your textbook or that your professor provided? Okay. T2 while we're told the final temperature is 110°C. Okay, we want to convert this into Calvin. So we get plus 273.15 Calvin. And then we're going to subtract the initial temperature Which we're told is 10°C. And again we're going to add 273.15 to convert to Calvin. Alright, working this out, this is going to give us a work W of 1496. jewels. Okay. The unit of mole times Calvin will cancel with the mole and the Calvin here we're left with the unit of jewel, which is a unit we want for work where units check out. Okay? And if we go back to the top And look at our answer choices and we see that we get answer choice B-1497 jewels. That's it for this one. Thanks everyone for watching. See you in the next video.