Question

(b) We would like to demonstrate that the appropriate free energy is minimized in thermodynamic equilibrium by considering a system at constant temperature and pressure, for which the Gibbs free energy G-U-TS+ PV is appropriate o Write down the first law of thermodynamics linking heat, q, to AU and work Au-grw i) du tfestdv ) du dsreu Tds-Pdv-) sPdV dus Write down an inequality relating the temperature-weighted entropy change, TAS to q ds ii) Use the result of (i) and (ii) to write down an inequality relating TAS to AU and work iii) Use the result of (ii) to obtain an inequality for AG when the system is released out of equilibrium and iv) undergoes spontaneous random changes. Explain concisely why your result in (v) implies that the system has reached a state of thermal equilibrium v) if G has reacheda minimum.

Answer 1

as ourq b) is first Law of Thermodynamied is mathematically exporessed Durqtw/-0, where so = change in internal enegy ar heat, we workdare i Inequity relating as and q for spontaneous reaction is, Ta temperature asa entropy change un) as Y & TASQ (q=su-w, fromo) & TASYBU-W - WYDO-TOS) relation between so TAS & w .

iv) Gou-TS +PN (given) differentiating both sides, we get! du-do-Tds - sdt tedu + vde at const T&P daco & de co 2 dae do- Tds & edu oh= so-TAS +PAV I we snow that W=-Pay at const P7 a sua so- TAS -W ) Dutw = BU-TOS – from three () wy au-TAS & DU-TAS cw – from Ahtwcw - до 1 - Ancol for spontaneous exh.