0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are and (c) volume V₃?

Video transcript

Hey, everyone. Let's go through this practice problem N mole of an ideal gas in a piston cylinder aperture experiences the transformations shown in the figure below, calculate the volume at point C. And we're given a little figure showing the different states of the gaffs and four multiple choice options to choose from. Option A 5.35 liters, option B 8.81 liters, option C 12.1 liters and option D 14.6 liters. OK. So for each state of a gas, we're told about variables such as the pressure, the volume and the temperature. If we want to find a relationship between these variables between the variables. For each state, we can use the combined ideal gas law which states that the pressure multiplied by the volume divided by the temperature will be constant. So it's equal constant. So for our purposes, since we're looking for a variable at state C, let's compare, let's use the combined ideal gas law to compare the variables at state C with the variables at state A, since we're given all three variables for state A, so I'm gonna say net P sub A multiplied by V sub A divided by T sub A. So the variables at state A are equal to the variables of state C. So that's P sub C multiplied by V sub C divided by T sub C and V sub C is what we want to find. So we're going to algebraically solve this for V sub C and we can do that by multiplying both sides of the equation by T sub C and then dividing both sides of the equation by P sub C. So what we find is a formula saying that V sub C is equal to P sub A V sub A T sub C divided by P sub C T sub A. So all we have to do now is plug in the variables given by the figure. So for P sub A that is six atmospheres, sub A, that's three liters bet sub CS 884 Kelvins and it's divided by P sub C which is 3. atmospheres multiplied by T sub A which is 320 Kelvins. If we put this into a calculator, then we find a volume of about 14.6 liters. So that is our answer 14.6 liters. And if you look at our multiple choice options, we can see that this agrees with option D. So option D is the correct answer to this problem. And that's it for this video. I hope this video helped you out if you think 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.