A 20.0-L volume of an ideal gas in a cylinder with a piston is at a pressure of 3.0 atm. Enough weight is suddenly removed from the piston to lower the external pressure to 1.5 atm. The gas then expands at constant temperature until its pressure is 1.5 atm. Find w.

Question

Accepted Answer

Hey everyone in this example, we're given a initial volume of 10 liters for an ideal gas under the pressure. 2.3 A t. M's. We're told this gas is compressed to a pressure of five A t M's at constant temperature. We need to calculate our value for work. What we should initially recall is that our value or our formula for work is that it's found from taking negative one times our value for our final pressure. And this is then multiplied by the difference in our volume. Now, according to this question, we're given our initial volume, we're given our initial pressure and were given a final pressure. However, we need a final volume as well. So we want to recall our formula for Boyle's Law which states that our initial pressure times our initial volume should be equal to our final pressure times our final volume. And so because we don't know our final volume, we would say that our final volume is equal to our initial pressure times, final volume divided by our final pressure. And so we would find our final volume by plugging in that initial pressure Given as 2.3 ATMs Multiplying that by our initial volume given us 10 l and then dividing this by our final pressure given as five A. T. M's. So our units of a TMS would cancel out leaving us with leaders, our final unit for volume And this is going to give us a final volume equal to 4.6 L. So now we can go ahead and find our calculation for work which again is given as our negative value for our final pressure which the problem tells us is five ATMs and then multiplied by our difference in volume. So for delta v difference in volume, we're going to take the final volume which we just found as 4.6 liters and subtract that from our initial volume given as 10 liters in the question. And so this is going to give us a value when we multiply our our units out of positive 27 80 M. Times leaders. However we want to recall that work is in units of jewels. And so we should recall the conversion factor that we have 101.3 jewels Equal to 1 M. Times leaders. So we're going to take our 27 80 M. Times Leaders and use that conversion factor. So in our denominator we should have won a. T. M. Time leader And then our numerator, we want our final unit in jewels equal to 101.3 jewels. So we are able to now cancel out a. T. M's. Times leaders leaving us with our final unit as jewels. And this gives us our value for work Equal to a value of 20 or sorry this should be 2735.1 Jules. And so this will be our final answer as our value for work to complete this example. So I hope that everything be reviewed was clear. If you have any questions, please leave them down below, and I will see everyone in the next practice video.

A 20.0-L volume of an ideal gas in a cylinder with a piston is at a pressure of 3.0 atm. Enough weight is suddenly removed from the piston to lower the external pressure to 1.5 atm. The gas then expands at constant temperature until its pressure is 1.5 atm. Find w.

Verified Solution

Key Concepts

Ideal Gas Law

Work Done by a Gas

Isothermal Process