0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are (a) temperature T₁,

Video transcript

Hey, everyone. Let's go through this practice problem. 0.25 moles of helium experiences the transformation shown in the figure below using the information given in the figure find the temperature of the gas at point A. So the figure shows a pressure volume diagram with three different states of a gas giving us variables about each state including the pressure volume and temperature. We have four multiple choice options to choose from. Option A 77 Kelvins option B 100 and Kelvins option C 780 Kelvins and option D 920 Kelvins. The problem is asking us to find the temperature of the gas at point A. So it's the variables related to state A that are most relevant to us here. Since we're trying to find the temperature, we can relate the temperature to the other variables we're given, including the number of moles of the gas. By using the ideal gas law which states the pressure of a gas multiplied by its volume is equal to the number of moles of a gas multiplied by the ideal gas constant multiplied by its temperature. And since that temperature T is what we want to find we can solve for that by algebraically rewriting the ideal gas law to solve it for an equation of T. And doing that tells us that the temperature T is equal to the pressure multiplied by the volume divided by the number of moles multiplied by the ideal gas constant. So all those variables have been given to us in the problem, but not all of them have been given to us in units that are useful to us. Because in order for the ideal gas constant to work, we need pressure in units of past Kells, not atmospheres, we're told that the pressure at state A is eight atmospheres. So we're going to want to convert that into pascals by using the fact that 1.13 multiplied by 10 to the power of five pascals corresponds to one atmosphere. And so if we put that into a calculator, then we find that the pressure at state A can better be written as 810,400 pascals, we'll also want to do a unit conversion on the volume at state A V sub A because we're given the volume as two liters. But with the ideal gas constant, we need that in units of cubic meters. So recall that for one cubic meter, there are 1000 liters. So we can use that to apply a unit conversion. And we find that the volume of state A is best written as 0.2 cubic meters. Now we have all the variables that we'll need to plug into the ideal gas constant or the, the ideal gas law. And so what we find using the equation and I'm going to specifically specify that these are state A variables we're looking for. So T sub A is equal to P sub A, the pressure at state A multiplied by V sub A divided by N R. So now just plug in the things you were given in the problem. So the pressure P sub A we discussed earlier is 810,400 pascals and V seven A. As we just decided, it decided is 0.2 cubic meters. And all this is being divided by the number of moles N which is given to us directly in the problem as 0.250 moles multiplied by the ideal gas constant, which we'll recall is equal to 8. jewels per mole Kelvins. So if we put all this into a calculator, then we find a number of moles and we find a, a temperature of approximately Kelvins. So that could be our answer to this problem. And if we look at the multiple choice options, we're given, we can see that this agrees with option C 780 Kelvins. So option C is the correct answer to this problem. And that is it for this problem. I hope this video helped you out. If you believe you need more practice, please check out some of our other videos which will give you more experience with these types of problems, but that's all for now. I hope you all have a lovely day. Bye bye.