n moles of an ideal gas at temperature T1 and volume V1 expand isothermally until the volume has doubled. In terms of n, T₁ , and V₁, what are (b) the work done on the gas, and

Video transcript

Hi, everyone in this practice problem, we're being asked to determine the work done on the guest. We will have an experiment conducted by a group of engineers investigating the behavior of an ideal guest with N moles of the guests in a sealed container at the temperature of te one and a volume of pe one. The engineers expand the container isotherm keeping the temperature constant until the volume tripled. We're being asked to calculate the work done on the gas during this process. In terms of NP one and P one, the options given R A RT one Ln two B negative N RT one Ln three C RT one Ln three and D negative N RT one Ln two. So the work done in an isothermal process is going to be given by the equation if we recall of W which will be the work equals to negative N multiplied by R multiplied by tt multiplied by the Ln of P two divided by P one. In this case, N is the number of moles R is the ideal guess constant D is the temperature P two is the final volume and P one is the initial volume. In the problem statement, it is given that the volume is going to be tripled by the isothermal process. So P two will be equal to three P one. So what we can do next is just substitute the P two into this equation. So that W will be equal to negative N multiplied by R multiplied by T multiplied by Ln of P two will be three P one divided by P one and we can cross out the P ones so that we will get the equation for the work done to then be equal to negative N multiplied by R multiplied by T multiplied by Ln of three. So the work done on the gas during this process in terms of NP one and P one will then be given by W equals to negative N multiplied by R multiplied by T one multiplied by Ln of three. And that will be the final answer to this particular practice problem which will correspond to option B in our answer choices. So option B will be the answer to this particular practice problem. And that'll be it for this video. If you guys still have any sort of confusion, please feel free to check out our adolescent videos on similar topics on our website. But other than that, that'll be it for this video. And thank you.