# Thermodynamics - DOC by abdollahifar

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```									Thermodynamics Essential features: –Thermodynamics: what material wants to do (forces) – Kinetics: what it can do, and how quickly Study – Thermodynamics • Properties • Equilibrium phase diagrams – Kinetics • Continuous: heat and mass diffusion • Structural phase transitions – Environmental interactions • Wetting and catalysis • Corrosion The conditions of equilibrium and stability – Equilibrium → no desire for change – Deviation from equilibrium → driving force for change – Beyond limits of stability → must change • Internal equilibrium – T, P, {μ} are constant – Deviation drives heat and mass diffusion • Global equilibrium – Thermodynamic potential is minimum – Deviation drives structural phase transformations

First Law of Thermodynamics Defines “internal energy”, E • Energy is conserved dE = dW + dQ
dW = work done (chemical + mechanical +electromagnetic)

dQ = heat transferred (thermal work)

– Energy transferred to one material is taken from another

Second Law of Thermodynamics Defines “entropy”: S • Entropy is associated with – Evolutionary time (most fundamental) – Heat – Randomness (information) • When a system is isolated, S can only increase – Any system is isolated when its surroundings are included A Simple “Adiabatic” System

Simple system in thermally insulated container • Can do mechanical work – Reversibly, with a frictionless piston – Irreversibly, with a paddle wheel – But no thermal interaction because of insulation • This is called an “adiabatic” system – An isolated system is one example of an adiabatic system

Change of State in an Adiabatic System
Moving piston generates E-V curve • Turning paddle wheel – Raises E at constant V – Changes the reversible E-V curve

System moves to new E-V curve System can never return

Entropy = Time (State of Evolution)
States (E,V) on a reversible curve have a common property: call it entropy (S) • Assign a numerical value of S to each curve such that S is continuous • Then S = S(E,V) measures the evolutionary time of the state (E,V) – S can only increase – S divides past (S’<S) from future (S’>S)

If the change of state is reversible (no friction, etc.) –

dW = -PdV

dQ = dE - dW = TdS (reversible thermal “work”)

Can measure S from heat added in a change of state

Statistical Entropy Isolated system E,V with given E,V Let Ω(E,V) be the number of distinguishable states for given (E,V) – Distinguishable ways of arranging atoms – Distinguishable ways of distributing energy or momentum among atoms • Can show that a good measure of the entropy is S(E,V) = k ln[Ω(E,V)] → Can calculate entropy from a knowledge of the system

Entropy of a Multicomponent System N1, N2, … , Nn = {N}

The entropy is

S = S(E,V,{N})

where μk is the “chemical potential” of the kth component

The Fundamental Equation The entropy function (“fundamental equation”)

The energy function (alternate form of the “fundamental equation”) E = E(S,V,{N})

The quantities S, V, E, {N} are fixed by the function, the “intensities” (forces: T, P and {μ}) are given by its derivatives

The Fundamental Equation

Thermodynamic forces from derivatives of FE – T, P, {μ} – These can be controlled independently • Thermodynamic properties from second derivatives – Specific heat, compressibility, CTE – These are material properties 200_lecture_slides-8↑

Necessary Conditions for Internal Equilibrium: Thermal equilibrium: – Temperature is constant (T) • Mechanical equilibrium (for a fluid): – Pressure is constant (P) • Chemical equilibrium: – Chemical potential of each component is constant (μ k) Summary: Thermodynamic Potentials and Conditions of Equilibrium Isolated system: E, V, {N} controlled – Entropy, S(E,V{N}) = maximum • Thermal contact: T, V, {N} controlled – Helmholtz free energy, F(T,V,{N}) = E-TS = minimum • Thermomechanical contact: T, P, {N} controlled – Gibbs free energy, G(T,P,{N}) = E-TS+PV = minimum • Open contact: T, V, {μ} controlled – Work function, Ω(T,V,{μ}) = - PV = minimum – Or, equivalently. P = maximum

Thermodynamics of Simple Solids Ordinarily, P, V and {N} are controlled – P is atmospheric pressure, PV is negligible → G ~ F; use F = E-TS to assess equilibrium • For a one-component solid with fixed N,V

The specific heat, CV, determines F for given N,V The Specific Heat of a Solid CV behaves similarly for all solids – CV α T3 at low T – CV = 3Nk when T>ΘD (Debye T) – Sum of two effects • Electronic specific heat – Electrons excited to high energy states – Almost always small • Vibrational specific heat – Energy is absorbed in atomic vibrations – Dominant is almost all cases

Phase Transformation in a One-Component System

200_lecture_slides-10

Thermochemical Properties • Materials respond to – Thermal stimuli (temperature) – Chemical stimuli (composition or environment) – Electromagnetic stimuli (electric or magnetic fields) – Mechanical stimuli (mechanical forces) • Consider the first two together – Response to thermal or chemical stimuli defines thermochemical properties The fundamental equation – There is a single equation that contains all thermodynamic information S = S(E,V,{N}) (for a multicomponent fluid) The conditions of equilibrium and stability S = maximum value for given E,V,{N} – Criteria that can be used to test equilibrium and stability – Deviation from equilibrium => driving force for change

The entropy of an isolated system can only increase For an isolated system in equilibrium, there must be no small change of state that increases its entropy

Equilibrium When the System is not Isolated: Thermodynamic Potentials • Consider three cases: • Material interacts thermally with environment: – Equilibrium requires that the “Helmholtz free energy” be a minimum F = E - TS • Material interacts thermally and mechanically with environment: – Equilibrium requires that the “Gibbs free energy” be minimum G = E - TS + PV • Material interacts thermally and chemically with environment – Equilibrium requires that the “work function” be minimum

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