Assume that you have a cylinder with a movable piston. What would happen to the gas pressure inside the cylinder if you were to do the following? (c) Decrease the volume by 45% at constant T

Video transcript

Hi everyone. This problem reads consider a cylinder with a movable piston. If you're able to do the following, what would happen to the gas pressure inside the cylinder, reduce the volume by 35% while keeping the temperature constant at T. Okay, so the question that we want to answer here is what would happen to the gas pressure inside the cylinder. Okay, so the equation that we're going to want to reference to solve this problem is N r T is equal to the initial pressure times the volume the initial volume which is equal to the final pressure times the final volume. Okay. And in this case we're interested in the value for final pressure. Okay. So we need to isolate this so that we're solving for final pressure when we isolate this, we get the final pressure is equal to the initial pressure times the initial volume over the final volume. All right, so let's go ahead and write down what we're given. Okay, so we're going to assume that the initial volume and the initial moles is one for easier comparison to the final amounts. Okay, so our initial pressure is one atmosphere, Our initial volume is one leader and our final volume is going to be one leader minus 30 or 300.35 liters because we're told that the reduced the volume by 35%. So we're going to convert that 35% to a decimal so minus 35.35 liters gives a volume of 0.65 liters. Okay, so now we have all our values and we can go ahead and plug them in. So our final pressure is going to equal the initial pressure, which is one atmosphere times the initial volume one leader times the final volume 0. liters. So the answer that we're going to get for the final pressure is 1. atmospheres. So what this means is that the gas pressure inside the cylinder increases by 1.5 times. Okay, so let's go ahead and write that the gas pressure Increases by 1. times. So this is going to be our final answer in terms of what would happen to the gas pressure inside the cylinder. That's it for this problem. I hope this was helpful.