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 pressure inside the cylinder if you were to do the following?
(d) Halve the Kelvin temperature and triple the volume

Accepted Answer

Welcome back everyone. We're told to suppose a gas sample is contained in a syllable with a cylinder with a movable piston. The kelvin temperature of the gas is doubled while its volume is reduced by one third identify the change in pressure of the gas. So what we're going to think of is our combined gas law Where we have our initial pressure multiplied by the initial volume divided by the initial temperature equal to our final pressure, multiplied by final volume, divided by final temperature. Now, according to the prompt, we need to isolate for the final temperature or sorry, the final pressure P two. So isolating for final pressure. We'd see that we have initial pressure times initial volume times initial temperature divided by initial temperature, times final volume. Now, according to our prompt, we are going to be interpreting our final temperature as So we'll put an equal sign here, the initial temperature times two since it's doubled. Also, according to our prompt, we're interpreting our final volume As our initial volume times 1/3 since it's reduced by 1/3. So we're going to incorporate these substitution into our formula for solving for the final pressure. So what we're going to have is that our final pressure is equal 2, 2, multiplied by initial pressure, times initial volume times initial temperature divided by 1/3 times our initial volume times our initial temperature. And sorry, that's just a one there. So now we can see that we can cancel out our terms for initial volume and initial temperature and what we're left with is that our final pressure is equal to six, multiplied by the initial pressure. And so we would agree with for our final answer choice D, which states that the pressure will increase by a factor of six. So D. Is going to be our final answer as the change that we identify according to our final pressure of our gas. If you have any questions, please leave them down below, and I will see everyone in the next practice video.

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