Assume that you have a cylinder with a movable piston. What would...

Question

Assume that you have a cylinder with a movable piston. What would happen to the gas volume of the cylinder if you were to do the following?
(d) Double the Kelvin temperature and double the pressure

Accepted Answer

Welcome back everyone in this example. We're supposing a gas sample is contained in a cylinder with a movable piston. The Kelvin temperature of the gas is reduced by 1/4. While its pressure is tripled, we need to identify the change in volume of the gas. So what we want to recall is our combined gas law where we recall, we have our initial pressure multiplied by initial volume divided by initial temperature set equal to final pressure times, final volume divided by final temperature. And now according to our prompt, We're going to be interpreting the final temperature as 1/4 times our initial temperature T one. And we're also going to be interpreting our final pressure as three times the initial pressure. So because we need to isolate for final volume, we're going to say that our final volume V two is equal to our initial pressure times initial volume times and final temperature T two divided by our final pressure, multiplied by our initial temperature. And so we're going to substitute these definitions here from the prompt for T two and P two. So that we can now say that our final volume is equal to 1/4, multiplied by our initial pressure times our initial volume times our initial temperature divided by three, multiplied by our initial pressure, times our initial temperature. And so now we can cancel out our terms for initial pressure and initial temperature and what we're going to be left with is that our final volume is equal to 0.083 times our initial volume. Which will therefore say that we have an increased volume. And so we would confirm that our final answer is going to be choice a, which states that the final volume is .083 times the initial volume. So I hope everything I went through is clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

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