0.0050 mol of gas undergoes the process 1→2→3 shown in FIGURE EX18.37. What are (b) pressure p₂,

Video transcript

Hey everyone, let's go through this practice problem. An ideal gas of mass M follows the transformations shown in the figure below using the information given in the figure find the pressure at point B. So we're given a figure showing the three states of the problem with information about some of the variables for each state including pressure, volume and temperature. We're also given four multiple choice options, option A 2.3 atmospheres, option B 4.1 atmospheres, option C 8.7 atmospheres and option D atmospheres. The point of this problem is to find the pressure at point B. So we're going to have to find some comparison between the variables we're given for state B and compare them to the variables we're given in the other state. Recall the combined version of the ideal gas law which states that the pressure of a gas multiplied by its volume and divided by its temperature is constant. We can use this formula to compare the variables between two different states which will allow us to solve for the pressure or what we want to find P sub B. Since we're given all three variables for state A, let's use the combined ideal gas law to compare the variables of state B to the variables of state A. So let's set this up. So P sub A, the pressure for state A multiplied by V sub A divided by T sub AY is equal to P sub B multiplied by V sub B divided by T sub B. We're trying to solve for P sub B. So let's algebraically solve this equation for P sub B by multiplying both sides of the equation by T sub B and dividing both sides of the equation by V sub B and W. And we find a formula for P sub B of P sub A multiplied by V sub A multiplied by T sub B all divided by V sub B multiplied by T sub. So now let's plug in the variables we have into this equation. So P sub B is equal to P sub A which the graph tells us is six atmospheres multiplied by V sub A three liters multiplied by T sub B which the graph tells us is 620 Kelvins all divided by V sub B which the graph tells us is four liters multiplied by T Sabe or 320 Kelvins. If we put this into a calculator, then we find a pressure for state B of about 8.7 atmospheres. So that is our answer to this problem. And if we look at our multiple choice options, we can see that this is what option C says 8.7 atmospheres. So option C is the final answer to the 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 tutoring videos which will give you more experience with these types of problems and that's all for now and hope you have a good day. Bye bye.