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Welcome to thermodynamics in energy engineering week 5.
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We are going to introduce free energy functions this week.
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To define free energy functions and their relations to reversibility,
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let's start from the entropy and the criteria for the reversibility determined by the entropy function.
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The entropy of a closed system is defined by delta Q over T. The criteria for the reversibility is shown here.
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The total entropy change, which is a sum of entropy change of a system and surrounding,
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is zero for the reversible process. For the irreversible process, the total entropy change is positive.
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Therefore, the total entropy change of a process determines reversibility. It's sign is the determinant.
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Therefore, to determine reversibility, we need information on surrounding,
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the entropy change of the surrounding. Then, can we tell reversibility only with the system properties?
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To see if we can, let's interpret this criteria at constant pressure process first.
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At constant pressure, the heat Qp is the enthalpy change.
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Then, entropy change of surround is the actual heat over T, so it is - dH over T.
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The total entropy change, the summation of entropy change of a system + entropy change of surrounding
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can be written like this. dS system - (dH system over T). It is summarize as 1 over T times (TdS-dH).
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So, TdS - dH determines the sign of total entropy changes. If it is positive,
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it is the spontaneous process at constant P. If it is zero, then the process is reversible at constant P.
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So, at constant pressure, TdS - dH can be the criteria for reversibility.
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Here, let's define new thermodynamic function for setting up criteria for reversibility.
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Let's set dG as - d (TS-H). If the temperature is constant, we can write it as - (TdS-dH).
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Define Gibbs free energy like this. G of a system equals H - TS.
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Then, G is defined only with the system properties such as enthalpy, entropy, and temperature.
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Therefore, the reversibility at constant temperature and pressure can be determined
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by Gibbs free energy thus with system properties only.
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The criteria is summarized like this. When dG is zero, it is a reversible process,
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and it is equivalent to delta S total is zero.
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The negative dG is equivalent to positive delta S total for the spontaneous process.
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If dG is positive, thus delta S total is negative,
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it is a process that will not proceed spontaneously and need energy for that process to happen.
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For the chemical reactions at constant temperature and pressure,
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the Gibbs free energy change of the reaction is the Gibbs free energy difference
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between the products and the reactants.
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Let's consider the second case. We are looking at the criteria for reversibility at constant volume process.
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The heat is internal energy change at constant volume.
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So the total entropy change is written like this. dS total is dS system - dU over T.
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The criteria for reversibility is like this. If this function is zero, then the process is reversible.
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If this is positive the process is spontaneous.
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Here, we see the new function for reversibility criteria as before. It is TdS - dU.
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So, at constant volume, TdS - dU can be the criteria for reversibility.
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At constant temperature also, TdS - dU can be written as - d (U-TS) and let's set it dF.
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Here, Helmholts free energy is defined like this. F equals to U - TS at constant volume and temperature.
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As in Gibbs free energy, F is defined only with the system properties.
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So the reversibility at constant T and V can be determined with system properties only by F,
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the Helmholtz free energy. The reversibility conditions are similar to the Gibbs free energy case.