A gas at 100°C fills volume V₀. If the pressure is held constant, what is the volume if

(a) the Celsius temperature is doubled

Question

A gas at 100°C fills volume V₀. If the pressure is held constant, what is the volume if

(a) the Celsius temperature is doubled

Accepted Answer

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 dry ice sublimes to form a gas that occupies volume V at 52 degrees Celsius, if the pressure remains constant and the temperature triples to degrees Celsius find the new volume. So it sounds like our end goal is to find the new volume. So we're given some multiple choice answers. Let's read those off to see what our final answer might be. A is V unchanged. B is three V C is 1.3 V D is 1.1 V E is 0.33 V and F is 0.61 V. Awesome. So first off note that dry ice is another name for solid carbon. And since it sublimes into a gas and it doesn't not melt into a liquid. So assuming if carbon dioxide behaves like an ideal gas, we could state that the pressure will be constant. So P equals constant. So the pressure will remain constant. So thus we can recall and use Charles Law, which we call that equation one. So that states so Charles Law, I should say Charles Law states that the initial volume divided by the initial temperature is equal to the final volume divided by the final temperature. So our angle is to solve for the final volume. So we must rearrange equation one Charles Law to solve for the final volume. So let's call it equation two. So the final volume, when we just solve for final volume, on one side, we should get the final volume is equal to the initial volume multiplied by the final temperature divided by the initial temperature. So before we can solve for the final volume, we must convert our initial temperature and our final temperature from degrees Celsius to Kelvin. So we need to recall the unit conversion for Kelvin. So let's do that really fast. So let's start with the initial temperature. So as you should recall, all we have to do to convert degrees Celsius to Kelvin is we take the degrees and Celsius and we add 273. So when we take 52 plus 2, 73 we should get 3 325 Kelvin and then doing the same for the final temperature. So our initial temperature is 325 Kelvin. So doing the same thing for final temperature 156 plus 2, 73 is, our final temperature was 156 degrees. So I'll pause here for a split second. So note, we do not have to multiply by three. Since the prom states, the temperature triples to 156 degrees Celsius. So don't let that trick you. OK. So when we add 156 plus 2 73 our final temperature should be 429 Kelvin. OK. So to find our final solution for the final volume, let's plug in all of our numerical values. So V F equals the initial volume multiplied by our final temperature was 429. Kelvin divided by our initial temperature which was 325 Kelvin. And note that as stated in the problem that the volume is V. So V I equals V. So our final answer will be 1.3 B. OK. So our final answer is 1.3 V where B represents the volume. So let's go back up here. So that means that our final answer is C 1.3 V. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

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

Verified Solution

Key Concepts

Charles's Law

Absolute Temperature

Gas Behavior Under Constant Pressure