WEBVTT
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Let's look at one of the most essential equations in thermodynamics. There are a number of state functions
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related to energy in thermodynamics. They are called thermodynamic potentials.
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The four most common thermodynamic potentials are U, H, G, and F.
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We only consider P - V work in energy functions for thermodynamic potentials in the following.
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The most fundamental potential is the internal energy U.
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dU is reversible heat + reversible work. And it is TdS - PdV. Let's define enthalpy. H is U + PV.
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Expand the differential. Then it is dU + PdV + VdP. Insert the dU above, then, it becomes TdS + VdP.
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Gibbs free energy G is H - TS. Thus its differential is dH - TdS - SdT.
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Insert the dH above, then, dG becomes - SdT + VdP. F is U - TS. So its differential is dU - TdS - SdT.
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Again, insert dU above, then dF becomes - SdT - PdV. The summary is shown.
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The total differential of thermodynamic potentials are like this.
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dU is TdS - PdV, dH is TdS + VdP, dF is - SdT - PdV, and dG is - SdT + VdP.
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Let's first look at the property of G. The dependence of G on temperature and pressure
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can be graphically interpreted from the thermodynamic potential equation. G is H - TS.
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And its total differential dG is - SdT + VdP. At constant pressure, dG is - SdT.
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So the dependence of G on T at constant pressure is - S. Let's graphically represent it.
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It is one example of gibbs free energy versus temperature curve. The slope of this curve is - delta S.
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At constant temperature, dG is VdP. So the dependence of G on P at constant temperature is V.
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Let's graphically represent it. It is one example of gibbs free energy versus pressure curve.
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The slope of this curve is delta V.