Achieve Week 4 #14

[Do Yeun Park]

For finding pathway A for problem 14, could someone explain why we use w = -nRT ln (Vfinal/Vinitial) formula?

[Shria G 2D]

Hi,
I think we use that formula to find work everytime it says it is reversible, isothermal expansion. I think it is because in reversible, isothermal expansion, the external pressure is changing by infinitely small amounts which means the volume also changes by infinitely small amounts (dV). The internal pressure is approximately equal to the external pressure for each step so if you sum up all the work done by the infinitely many steps, you get w = -integral(P dV). It is a definite integral from Vinitial to Vfinal. If you substitute P and solve the equation, you eventually get w = -nRT ln (V2/V1). I think this was mentioned in the wednesday lecture if you want a longer explanation but I hope this helps!