Assume that you have a sample of gas in a cylinder with a movable piston, as shown in the following drawing:

Redraw the apparatus to show what the sample will look like after (c) the temperature is decreased from 300 K to 200 K and the pressure is decreased from 3 atm to 2 atm.

Video transcript

Hi everyone. This problem reads shown below is a gas sample contained in a cylinder with a movable piston. The temperature is increased from 200 kelvin to 400 kelvin while the pressure is decreased from 2.6 atmospheres to 1. atmospheres, which of the following images illustrates the gas sample after. Okay, so we want to know which illustrates the gas sample after and were given initial and final temperatures and pressures. So the equation that we're going to want to use to solve this problem is P one times V one over T two, Which these represent pressure volume and temperature is equal to P two V 2 times T two. And in this case we want to solve for V two, we want to know the volume of the gas sample afterwards. So we need to rearrange this equation so that it is solving for V two. So when we rearrange the equation we're going to get V two is equal to P one, V one, T two over P two T 1. So, let's take a look at what's given in the problem. What's given in the problem is P1 is equal to 2.6 atmospheres. P two is equal to 1. atmospheres. T one is equal to 200 Calvin And T two is equal to Kelvin. So we have everything that we need to figure out the final volume or how much the final volume is increased. We don't need V one necessarily and you'll see why once we plug everything in. Okay, so let's go ahead and plug in everything. So we have V two is equal to P one which is 2.6 atmospheres times T 1 Calvin. Excuse me? So wait, P one is 2.6 atmospheres times the one which we Don't need. So we'll just go ahead and write V one, T two is 400 Kelvin over P two, which is 1.3 atmospheres times T one is 200 kelvin. Okay, so that's it right there. Excuse me for the confusion. So we don't need V one, so we're just going to leave V one as V one there. So once we do this calculation we get V two is equal to or times the one. Okay, so what that means is the final volume is four times the one. So the final volume increased. So looking at the original picture appear, we want to know which one's going to illustrate the gas sample after and we want the final volume increasing. So the answer choice that is going to represent the volume increasing is going to be Image C. Okay, so Image C is going to be the correct answer for this problem and that is it for this problem. I hope this was helpful