And that suggests then, that we should define yet another state function.

This, the Gibbs free energy. G which is equal to U minus TS plus PV

and we have the condition for spontaneity, at constant temperature and

pressure, that DG is less than or equal to 0.

Again I'd like to digress momentarily and talk a little bit of the history of

thermodynamics. And give you a little more introduction

to Josiah Willard Gibbs. So in 1863, Gibbs received the first

Ph.D. In the United States that was awarded in

the field of engineering and indeed he was the fifth person to receive a Ph.D.

In any field in the United States and he received that degree from Yale College.

He spent all of his professional life at Yale college actually.

And he had inherited some money from his family.

So, he worked as a faculty member for free for many years for Yale until after

he had achieved a certain measure of scientific fame.

Johns Hopkins university offered him $3000 a year as salary.

Yale retained him with a $2000 dollar a year offer because, I guess he just

really like New Haven, Connecticut. So, he spent all of his career there, and

he did fundamental work in an amazing number of areas.

Gears, brakes, steam engines, vector calculus, optics, statistical mechanics.

And. What was sort of remarkable, or a little

sad maybe in some ways is that he was virtually unknown in the United States,

even though he had an enormous reputation in Europe.

Where much of the work in science and engineering was going on during that time

period. So Max Planck in fact said of him at one

point, Gibbs is among the most renowned theoretical physicists of all times and

if Planck says that. That's a measure of some respect.

And then there was Albert Einstein, who said Gibbs is the greatest mind in

American history. And again, given the person saying that,

you have to imagine that Gibbs sort of had it going on.

Well, so I mentioned for Helmholtz, that, Germans honor their scientists with

stamps, for instance. You know stamps in the United States, you

got to get over a pretty high bar to be on a stamp.

But first, Gibbs did have a ship named after him, so a U.S.

Naval research vessel and oceanographic research vessel was named after him and

was active in the 1960's. And then finally he achieved that level

of notoriety needed for philatelic memorialization, and so here is that

stamp that was issued in 2005, showing Gibbs later in life, so, I sort of love

this early picture with the particularly florid bow tie.

It's hard to get away with wearing one of those today.

But honoring his work as a thermodynamisict.

And this is actually a figure that appeared in a work of Maxwell's, we'll

see him in an upcoming lecture, that took some of Gibb's ideas and attempted to

portray them graphically. Alright, well, again, enough history

digression. Let's come back to the Gibb's free

energy. So here's the definition.

G is equal to U minus TS plus PV. And I want to emphasize the relationships

between the state functions we've seen so far.

So given that another state function, enthalpy is U plus PV.

We can also write that g is equal to h minus ts.

And that's actually a form that people are probably more familiar with from

early chemistry studies. We can also relate it to the Helmholtz

free energy. So a is equal to u minus ts.