Using the derived formula or the integrated formula

[Derreck Tang 2D]

Since both forms of the work of expansion formula give relatively the same answer, should one formula be used more than the other?

[Chem_Mod]

Assuming you are talking about the work equations w = -P*(V2 - V1) and w = - nRT*ln(V2/V1), we cannot use these two formulas interchangeably. w = -P*(V2 - V1) is the constant pressure work equation, and is used when work is done irreversibly against a constant pressure. w = - nRT*ln(V2/V1) is the constant temperature work equation, and is used when work is done reversibly against a constant temperature.

[Jeff Balian 2D]

Additionally, w = -nRT*ln(V1 / V2) is the isothermal reversible expansion of an ideal gas. This is derived from the ideal gas equation: PV = nRT. Substituting P for nRT / V in W = -P * delta V and integrating the equation equates to w = -nRT*ln(V1 / V2).