Thermodynamic potential: Thermodynamic equilibrium vs Thermal equilibrium

Thermodynamic potentials are “potential energy” defined as the capacity to do work. Because we can only measure certain properties of a system, thermodynamic potentials are used to measure its energy in terms of different variables. For example, we may know the system's pressure and temperature but not its volume or entropy. Thermodynamic potentials allow us to measure more system state variables. Internal energy U, enthalpy H, Helmholtz free energy F, and Gibbs free energy G are the four fundamental functions. They are "potential energy," which is defined as the ability to do work. We derive expressions for the differential form of four thermodynamic potentials from the first and second laws of thermodynamics. They are referred to as fundamental equations.

What does thermodynamic potential mean to me?

The first point to remember thermodynamic potentials define the potential energy of a system available to perform work. When all thermodynamic potentials are zero, the system is called, it is in thermodynamic equilibrium. The system has no energy to change. Thermodynamic variables link with each other through a number of equations state [EOS] based on the first and the second law of thermodynamics.

Explanation

Let me start with an easy-to-understand example.

Internal energy and enthalpy

Take a simple example. When you heat water to 100 degc at atmospheric pressure such that the vapor and water have the same temperature, water and steam have just reached thermal equilibrium because they have the same internal energy. But that does not mean they have the same total potential energy or same total energy or same enthalpy, dH = dU +PdV, H is enthalpy, U is internal energy, P is pressure and V is the volume. You have just accounted for the internal energy equating steam and water at 100 degc/1 bar pressure and not the work. Work is a component of the total energy as per the 1st law of thermodynamics. The difference, in why W [work] is accounted for separately in the fundamental EOS for energy conservation is simply because W is a path function and U is a state function.

So, coming back to the subject, at 100 degc, 1 bar pressure water and steam are just in thermal equilibrium. They still have the potential energy to perform work. They have still the ability to change over time. Therefore, at 100 degc/1bar pressure water -steam may be in thermal equilibrium but not in thermodynamic equilibrium. For thermodynamic equilibrium to happen not only there should be no change in internal energy but there is no change in the total energy or enthalpy of steam and water.

Let us look at all four thermodynamic potentials and try to understand what they mean.

Internal energy (U) is the capacity to do work plus the capacity to release heat, Δ U = Q + W, positive heat Q adds energy to the system and positive work W adds energy to the system.

Gibbs energy (G) is the capacity to do non-mechanical work, G = H - TS. Free energy change. dG accounts for a system’s potential energy at constant pressure to perform work after discounting entropy change, dS

Enthalpy (H) is the capacity to do non-mechanical work plus the capacity to release heat, H = U + W. ?Enthalpy accounts for the total potential energy or total energy or system without discounting entropy.

Helmholtz energy (F) is the capacity to do mechanical plus non-mechanical work. Helmholtz free energy is a concept in thermodynamics where the work of a closed system with constant temperature and volume is measured using thermodynamic potential. It may be described as the following equation: F = U -TS.

Why there are two free energies?

Gibbs and Helmholtz free energy: What do they mean?

Both represent the potential energy of a system to perform work after discounting entropy losses. The difference is Gibbs free energy is the potential energy at constant pressure while Helmholtz potential energy stands for the potential energy of a system at constant volume. In both the temperature is held constant.

Again, let us recheck what the four thermodynamic potentials mean.

From these meanings (which actually apply in specific conditions, e.g., constant pressure, temperature, etc.), we can say that ΔU is the energy added to the system, ΔF is the total work done on it, ΔG is the non-mechanical work done on it, and ΔH is the sum of non-mechanical work done on the system and the heat given to it. Thermodynamic potentials are very useful when calculating the equilibrium results of a chemical reaction, or when measuring the properties of materials in a chemical reaction. The chemical reactions usually take place under some constraints such as constant pressure and temperature, or constant entropy and volume, and when this is true, there is a corresponding thermodynamic potential that comes into play. Just as in mechanics, the system will tend towards lower values of potential and at equilibrium, under these constraints, the potential will take on an unchanging minimum value. The thermodynamic potentials can also be used to estimate the total amount of energy available from a thermodynamic system under the appropriate constraint.

Credit: Google