A gas at 100°C fills volume V₀. If the pressure is held constant, what is the volume if (b) the Kelvin temperature is doubled?

Video transcript

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. So a sample of an ideal gas has a volume B at 80 degrees C when the pressure of the gas remains fixed, find the volume when the Kelvin temperature is 1/5 the initial Kelvin temperature. Awesome. So we're given some multiple choice answers. So let's read those off to see what our final answer might be. A is 1.6 B B is 25 BC is 0.40 V D is V unchanged, E is 5.0 V and F is 0.20 V. Awesome. So first off, let's note that at the pressure, the gas remains fixed, that means that pressure remains constant. And if the pressure remains constant, we can recall and use Charles Law which states that the initial volume divided by the initial temperature is equal to the final volume divided by the final temperature. Awesome. So our end goal is to find the final volume. So let's rearrange Charles Law to solve for the final volume, let's call it equation one. So when we rearrange Charles Law to solve for the final volume, we should get the following. So the final volume is equal to the initial volume multiplied by the final temperature divided by the initial temperature. So note that the final temperature is 1/5 the initial temperature. So we can rewrite equation one as follows. So the final volume equals 1/ the initial volume. And note that as stated in the problem that V I, so the volume of V so V I equals V. So that means our final answer is 0.20 V. So our final answer is 1/5 of the final volume. Awesome. So that means our final answer is F 0.20, V is 1/5 when you plug it into a calculator equals 0.20. Thank you so much for watching. Hopefully that helps and I can't wait to see you in the next video. Bye.