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The fundamental equation

المؤلف:  Peter Atkins، Julio de Paula

المصدر:  ATKINS PHYSICAL CHEMISTRY

الجزء والصفحة:  ص 102-103

2025-11-06

535

The fundamental equation

We have seen that the First Law of thermodynamics may be written dU = dq + dw. For a reversible change in a closed system of constant composition, and in the absence of any additional (non-expansion) work, we may set dwrev=−pdV and (from the definition of entropy) dqrev=TdS, where p is the pressure of the system and Tits tempera ture. Therefore, for a reversible change in a closed system, dU=TdS−pdV , However, because dU is an exact differential, its value is independent of path. Therefore, the same value of dU is obtained whether the change is brought about irreversibly or reversibly. Consequently, eqn 3.43 applies to any change—reversible or irreversible— of a closed system that does no additional (non-expansion) work. We shall call this com bination of the First and Second Laws the fundamental equation. The fact that the fundamental equation applies to both reversible and irreversible changes may be puzzling at first sight. The reason is that only in the case of a reversible change may TdSbe identified with dqand−pdVwith dw. When the change is irreversible, TdS>dq (the Clausius inequality) and −pdV>dw. The sum of dw and dq remains equal to the sum of TdS and−pdV, provided the composition is constant.