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One is used when the system is at constant pressure (irreversible expansion) (w=-pdeltaV) and the other is used when pressure is not constant (usually isothermal reversible expansion) (w=-nRT*ln(Vf/Vi)).
W=-PdeltaV is utilized when pressure IS constant which was shown in lecture through a definite integral because we could factor out the constant of pressure and we are left with the integral dv which just means V2-V1 if we put it into a definite integral. We use the other equation -nRTln(V2/V1) when pressure IS NOT constant, and the derivation of this formula was shown in class today.
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