Question

Q2) In class we showed that you can re-express the Second Law in terms of a system's Gibbs Free Energy. In fact, we can choose any combination of thermodynamic quantities. We can instead choose to define the Combined Potential Φ as Φ-U-TS-μ.NA-μΒΝ. Íor a system that contains molecules of types A and B a) Show that the thermodynamic identity for the Combined Potential is dDSdT- PdV- N.dyl N.dyua. (Hint: the First Thermodynamic Identity for this system is Express entropy, the particle numbers, and pressure in terms of derivatives of the Combined Potential. Make sure that you state which quantities are constants for each quantity c) Consider a system of fixed volume in contact with an infinite reservoir of heat that maintains a constant temperature and volume but can exchange particles of types A and B. If the entropy of the system is S, and of the reservoir Sr, then the total change in entropy can be written as dSTotal dSR . Show that the Second Law can be re-expressed as "the Combined Potential of a system tends to decrease" at constant temperature and chemical potentials Remember that the reservoir volume is constant, the total energy and numbers of particles A and B are conserved when summed over the reservoir and system, and that the chemical potentials of each species are equal in the reservoir and system when at diffusive equilibrium A and B

Answer 1

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