Lecture17A - (Free) Energies: Helmholtz and Gibbs(Chapter...

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(Free) Energies: Helmholtz and Gibbs (Chapter 22.1,22.2) For an isolated system, dS>0 Æ spontaneous process occurs. But how is an open beaker isolated? It isn’t, so we must consider Δ S of the surroundings as well. Then, Δ S universe = Δ S surr + Δ S sys >0 will determine spontaneity. This is a lot of work to determine if a process is spontaneous. there an easier way? Is there an easier way? Consider a real (not ideal!) system under isothermal conditions and at nstant V: U q w = + constant V: dU δδ () 0 constant V because / ext wP d V TdS dS q T δ = −= Since: d ( ) because q TdS ≤≥ and Then: so at constant V dU q TdS dU TdS =≤ at constant V U TdS 0 0 at constant T dU TdS dU T S −≤ Lecture 17 1 Let's define Helmholtz (free) energy A UT S ≡− = 0 dA where 0 at equilibrium dA = and 0 for a spontaneous process dA < The Helmholtz energy (based solely on the system) can tell us whether a process will occur spontaneously! The Helmholtz energy will continue to decrease for any spontaneous process until it reaches equilibrium, where A will be a minimum. Fig 22.1 Isothermal: - 0 Reversible equilibrium : 0 A UTS Δ=Δ Δ≤ Δ=Δ −Δ= Lecture 17 2 ( ) q Spontaneous irreversible: 0 AU T S Δ=Δ −Δ< U Δ S Δ A Δ Spontaneous?
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Lecture17A - (Free) Energies: Helmholtz and Gibbs(Chapter...

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