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Free energy functions

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

We can determine the reversibility of the process by looking at the total entropy change.

However, total entropy change is not the system property. We need information on the surrounding and that’s not very convenient thermodynamically. We need some system properties that can determine the reversibility. The free energy, such as Gibbs free energy and Helmholtz free energy, is the system property. Under a certain limited condition, their sign can be the criteria for the reversibility equivalent to the total entropy change. We derive at two important free energy functions, the Helmholtz free energy and the Gibbs free energy.

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Thermodynamics in Energy Engineering

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