Using the derived formula or the integrated formula
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Using the derived formula or the integrated formula
Since both forms of the work of expansion formula give relatively the same answer, should one formula be used more than the other?
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Re: Using the derived formula or the integrated formula
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.
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Re: Using the derived formula or the integrated formula
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).
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