What is an example of Gibbs free energy? [duplicate]

I know it is a letter $$G$$ in some equation. What I want to know is the example. Is it like chemical bond energy?

I read the Wikipedia article on Gibbs free energy but I couldn't understand it. I don't know what exactly the non-expansion energy is.

I would like explanations about what Gibbs free energy really is, preferably in a manner as if I were really watching the molecules and their interactions and movements.

Edit: For example, Microscopically, the internal energy can be analyzed in terms of the kinetic energy of microscopic motion of the system's particles from translations, rotations, and vibrations, and of the potential energy associated with microscopic forces, including chemical bonds.

Can you describe Gibbs free energy like this?

– SG8
Commented Apr 12, 2021 at 11:24
• I think this answer which I had written would suffice here. For this question, if you want examples, I can answer with that Commented Apr 12, 2021 at 11:36

Gibbs free energy is a thermodynamic potential which is derived using Legendre trasformation of $$U(S,V,N)$$ (fundamental relation) for a thermodynamic hydrostatic system.
$$U(S,V,N)\to G(T,P,N)$$ using Legendre transformation
$$G(T,P,N)=U-TS+PV$$
$$dG=dU-TdS-SdT+PdV+VdP \tag{1}$$
By first law of thermodynamics,
$$dU=dQ-PdV+\mu dN$$
Substitute $$dU$$ in (1),
$$dG=(dQ-PdV+\mu dN)-SdT+PdV+VdP$$
$$\implies dG=dQ-SdT+VdP+\mu dN$$
For a closed system ($$dN=0$$), at constant temperature and and onstant temperature
$$dG=dQ-TdS$$
For a reversible process, $$dQ=TdS$$, so $$dG=0$$
For an irreversible process, $$dQ, so $$dG<0$$
So, for a thermodynamic spontaneous process, gibbs free energy decreases.

So we can see that gibbs free energy is like gravitational potential energy, when an object falls down (it falls spontaneously), gravitational potential energy decreases.
Similarly for a closed system when changing its state spontaneously at constant pressure and constant temperature, then Gibbs free energy decreases.
So, in chemical reactions in which temperature is held constant (in most of the chemical reaction pressure is constant), value of $$dG$$ determines whether the process is spontaneous or not.

What's Gibbs free energy?

$$G=H-TS \ \ \ \text{Gibbs function}$$

Suppose a system in contact with surrounding at temperature $$T_0$$ and pressure $$p_0$$. If heat $$\delta Q$$ enters the system,

$$\delta Q=dU-\delta W -(-p_0dV)$$ where mechanical work added to the system from the work $$-p_0dV$$ done by the surrounding due to the volume change of the system.

$$T_0dS\geq \delta Q\Rightarrow \delta W\geq dU+p_0dV-T_0dS$$ $$\delta W\geq dA, \ \ \ \ \ A\equiv U+p_0V-T_0S\ \ \text{Availability}$$ $$dA\leq 0 \ \ \ \ \ \text{mechanically isolated system}$$

All processes will tend to force $$A$$ downwards towards a minimum value. Once the system has reached equilibrium, $$A$$ will be constant at this minimum level.

If the system at constant pressure and temperature

$$dG=dU+p_0dV+Vdp-T_0dS-SdT=dU-T_0dS+p_0dV$$ $$\Rightarrow dA=dG\leq 0$$ So we must minimize $$G$$ to find an equilibrium state and $$G$$ is said to be the Gibbs free energy.

Example: If a chemical reaction is carried out at constant pressure and temperature, so if the system is trying to minimize its availability, then we need to consider $$\Delta G$$. The second law of thermodynamics implies that a chemical system will minimize $$G$$, so that if $$\Delta G$$, the reaction may spontaneously occur.