Heat Q flows into a monatomic ideal gas, and the volume increases while the pressure is kept constant. What fraction of the heat energy is used to do the expansion work of the gas?

Video transcript

Hey everyone in this problem. We have a student heating a vessel and closing argon gas. Argon is going to absorb some amount Q. Naught of heat and expand at constant pressure. What we're asked to do is find the percentage of heat energy involved in the expansion work of art. Alright, So the first thing we want to notice is that we're told that this is at constant pressure, which tells us that this is an ice a barrick process, Nyssa, barrett conditions and in isolated conditions, recall that we can write work okay? S. P delta B. Okay, pressure times a change in volume. Now we're dealing with argon, we can assume that this is an ideal gas. So we know that we can also use our ideal gas law. Now let's recall the ideal gas law says that P delta V is equal to N. R. Delta T. Okay, so this P delta V can also be written as N R delta T. Okay, so we have now work. W. Is equal to n R delta T. K. So we've related the work to the temperature. Alright, So we're talking about heat energy. When we're talking about heat energy, we're thinking about quantity Q. And we're also talking about work. Okay, So how can we were like Q. And w. Well, the first law of thermodynamics tells us that the change in the internal energy U. Is equal to Q minus W. Okay. And in this case we're talking Q. Not. So let's just call it, you know. Alright. If we want to know the percentage of heat energy involved in the expansion of work, we need to know what is the heat energy. So Q not is equal to delta U. Plus the work W. All right. We know we're going to leave W alone because we're looking at the percentage involved in work. Okay. So we know that we're relating Q. Not to W. So, let's leave W alone. What can we what do we know about delta you in this situation? Remember that we have an ideal gas which means that delta U. The change in internal energy Can be written as C. V. Times delta T. Hm. Now we also know that the gas argon is mon atomic mon atomic. Sorry, on atomic Which means that c. v. is going to be 3/2 are. So this means we can write delta U. The change in internal energy as N. Times three halves are times delta T. Now we can write the Cv value using our the gas constant which we know. Mhm. Alright, now, comparing this to work, we found that work is equal to N. R. Delta T. And delta U. Is equal to three halves and our delta T. So that means that delta U. Is just equal to three halves times the work W. Alright, so let's use this in our equation for Q. Not here we have Q. Not which is equal to delta U. Which we know is three halves tons of work W. Okay. Plus W. So we get that Q. naught is equal to 5/2 times w. Alright good. So we've written now the heat energy in terms of the work. Okay now we just want to find what percentage is made up of that. Okay. So what we want to know is the percentage of heat energy involved in the expansion work. Okay. So we're gonna take the work. We're going to divide it by Q. Not the heat energy. Okay. We'll work. We're just leaving as W. And now we know Q. Not is five half W. Okay, dividing is gonna give us two fists, okay. or 40%. Okay. And so this is the percentage of heat energy involved in the expansion work. Okay so that's going to be answer. B. Thanks everyone for watching. I hope this video helped see you in the next one.