At a constant pressure of 0.905 atm, a chemical reaction takes place in a cylindrical container with a movable piston having a diameter of 40.0 cm. During the reaction, the height of the piston drops by 65.0 cm. (The volume of a cylinder is V=pr2h,wherehistheheight;1Latm=101.3J.) (b) What is the value in joules of the work w done during the reaction?

Video transcript

hey everyone in this example we need to calculate the work when a sample of an ideal gas is compressed from six liters to 1.50 liters against an external pressure of 2.50 ATMs and were given the following conversion factor. So we want to first recall the formula where work is equal to the negative value for pressure times the difference in the volume or delta v. And so we want to recognize that the key word here is the word compressed. And so what the word compressed is telling us is that work is done. Bye the system or sorry, by the surroundings on the system. So that that is what that keyword compression is telling us. Work is being done by the surroundings on our system. And so therefore work should be a positive value when the surroundings are doing the work on the system. And so what we would have Is that our value for work is equal to the negative value of the pressure given us 2.50 ATMs multiplied by the difference in volume. Where we take the final volume Given as 1.50 l And subtract from the initial volume given us 6.0 leaders. And so what we're going to simplify this to is work is equal to a value of negative 2.50 ATMs Multiplied by the difference between the volumes equal to negative 4.50 leaders. And so this gives us work equal to a positive value of 11.25 leaders times ATM when we multiply those units out. and so what we want to do is use that given a conversion factor because we want work to be in jewels. So we're going to multiply by the conversion factor. We're in our denominator. We should have one leader times A. T. M. Is equal to 101.3 jewels. So we're going to be able to cancel out leaders times ATMs leaving us with jewels, which is what we want. And so this gives us a value for work equal to 1,139.63 jewels of our work being done by the surroundings on our system. And so that will correspond to anti choice d. Being our final correct choice to complete this example. So I hope that everything we reviewed was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.