Textbook Question 4A.5 Part B

[Mia_Renna_1L]

Hi, could someone please explain part b of this question? What does it mean / what are we supposed to do when a gas is allowed to expand reversibly and isothermally to the same final volume? I also do not understand where the -nRT and lnV1/V2 in the equation come from?

Thanks!

[Chem_Mod]

When a gas expands reversibly and isothermally, it means that it is expanding at constant temperature. This means that we have to use the constant temperature work equation, which is w = -nRT*ln(V2/V1). This equation comes from the expression w = -P*dV. Since we are at constant temperature and not at constant pressure, we plug in P = nRT/V and get w = (-nRT/V)dV. Since we are at constant temperature, -nRT are all constants, and if we integrate the expression, we get that w = -nRT*ln(V2/V1).