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RTueOct07

# RTueOct07 - Thermodynamics Mauna Kea 1 The Helmholtz Energy...

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1 Thermodynamics Mauna Kea

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2 The Helmholtz Energy Before we start using G just consider, for completeness what happens at constant temperature and volume. Under these conditions dq can be equated with dU and we can say, at equilibrium. This expression is derived in an analogous way to the expression for the Gibbs energy, i.e. dH – TdS = 0 0 = - TdS dU
3 Equilibrium The expression U – TS is a state function and is called the Helmholtz energy. The Helmholtz energy and the Gibbs energy provide criteria for spontaneity and equilibrium. These energies decrease for spontaneous process. For a system at equilibrium, for a reversible process, no work is done and there is no change in free energy. 0 = - TdS dU TdS dU dA - =

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4 Helmholtz Energy – Interpretation at constant Temperature: TS U A - SdT TdS dU dA - - = TdS dw dq dA - + = TdS dq = for a reversible process dw dA =
5 Helmholtz Energy – the Work Function If a system does work, then dw is negative and therefore dA will also be negative. In general terms A is a measure of the maximum amount of work a system can do. The work produced in an isothermal transformation is less than or equal to the decrease in the Helmholtz energy. dw dA =

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6 Spontaneity and Equilibrium Reversible transformations are ideal. They involve infinitesimal changes which guarantee that the system does not lose equilibrium. Irreversible transformations are real. There is no physically achievable infinitesimal change – all changes are finite and therefore all changes are irreversible.
7 Maxwell James Clerk Maxwell (1831 – 1879) Einstein described Maxwell's work as the " most profound and the most fruitful that physics has experienced since the time of Newton. " Maxwell made contributions to electromagnetic radiation, photography, astronomy and thermodynamics At the age of 28 he published a paper that proved that, because the rings of Saturn were stable, they could not be completely solid or fluid.

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8 Maxwell’s Demon Maxwell's Demon was a thought experiment (gedankenexperiment) that Maxwell proposed to answer the question could the second law of thermodynamics be broken. http://ajs.net/maxwell.htm
9 Maxwell’s Equations A number of thermodynamic parameters cannot be measured directly. As a result these parameters need to expressed in terms of others that can be experimentally determined.

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10 Properties of a System A system has: Mechanical properties …. P and V Fundamental properties …. T, U and S Composite properties …. H, G and A
11 Fundamental Equations dU = dq +dw = TdS – PdV dH = d(U + PV) = dU + PdV + VdP dH = TdS – PdV + PdV + VdP = TdS + VdP dG = d(H – TS) = dH – TdS – SdT dG = TdS + VdP – TdS – SdT = VdP – SdT dA = d(U – TS) = dU – TdS – SdT dA = TdS – PdV – TdS – SdT = – SdT – PdV

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12 Definitions of dU, dH, dG and dA dU = TdS – PdV dH = TdS + VdP dG = VdP – SdT dA = – SdT – PdV These four equations are sometimes called the four fundamental equations of thermodynamics.
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