What is the scientific and social importance of Gibbs ‘Free Energy’?

Answer

Hi Tom,

That is a very interesting question you ask, but also a difficult one.

The Gibbs energy was not “discovered” as such, but defined by Josiah Gibbs (1883-1903). In thermodynamics you can prove that the Gibbs Energy (or G) is the maximum non-expansive work that a system can do. Expansive work is work done by an expanding gas. So non-expansive work is done in every other way except by an expanding gas.

Now what is the importance of this? This allows us to understand how the non-expansive work supplied by a system depends on the parameters of which this system is a function. This sounds rather abstract, and to fully understand this, you actually have to delve quite deeply into the mathematical background of themodynamics.

Let me just give one relatively simple example. You can prove that for the total differential of G, dG, holds:

dG = Vdp -SdT + ∑µ_idn_i

Here p is the pressure, V is the volume, S is the entropy, µ_i the chemical potential of particle i. µ_i is actually nothing more than the partial derivative of G to n_i, the number of moles of the particle i. With the sum sign ∑ we mean that we add up over all particles i that occur in the system.

Now if we operate a system at constant pressure, e.g. open to the atmosphere, then p is a constant, and consequently dp = 0

If we also keep the temperature constant, and that is not so difficult, if necessary you put the system in a thermostatic bath, then T is also a constant and so dT = 0.

This means that the above expression actually reduces to:

dG = µ_idn_i

This sum of terms only depends on the composition of the system, since only n_i occurs in it. So we can predict that a system can do work at constant pressure and temperature by changing its composition. An example of such a system is a battery. It can do work at constant pressure and temperature, simply by changing its composition.

I hope this somewhat answers your question.