MIT10_626S11_lec07

MIT10_626S11_lec07 - II Equilibrium Thermodynamics Lecture...

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Figure 1. Lattice sites with particles (black) and holes (white) The entropy of the system, defined by the great physicist Ludwig Eduard Boltzmann (1844- 1906) is where k B is Boltzmann’s constant and is the number of distinguishable (degenerate) states of the system. This assumes an “ideal solution” or “ideal mixture” of particles and holes. In the thermodynamic limit, we let N and N s -N go to infinity with the filling fraction held constant and use Stirling’s formula: II. Equilibrium Thermodynamics Lecture 7 : Statistical Thermodynamics Open circuit voltage of galvanic cell is To understand compositional effects on , we need to consider some simple statistical model. 1. Lattice gas We consider a “lattice gas” of N indistinguishable finite-sized particles ( N s -N indistinguishable holes) confined to a lattice of N s available fixed lattice sites. Notes by ChangHoon Lim (and MZB)
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f(x) ~ g(x) as , which we read “ f(x) is asymptotic to g(x) as means . The derivation of Stirling’s formula is shown at appendix. In the thermodynamic limit, Define the entropy density per site as with the filling fraction Therefore, in the thermodynamic limit, More generally, for an “ideal solution” of M components/species ( i=1, 2,…, M ) and holes where 2. Electrochemical potential Suppose the N particles have charge ze and feel a mean electropotential Then, the total Gibbs free energy is At constant T, P and , The electrochemical potential per particle, defined as the change in Gibbs free energy per particle, is where
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MIT10_626S11_lec07 - II Equilibrium Thermodynamics Lecture...

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