0:00
Okay, let's take a look at the key concepts from this last week.
So, first the Helmholtz fee energy is defined as A equals U the internal
energy, minus T the temperature, x S the entropy.
At constant temperature and volume spontaneous processes occur to minimize
the Helmholtz free energy. goes until the system is at equilibrium,
at which point only reversible process, that is those for which dA equals 0 will
occur. An analgous quantity is the Gibbs free
energy, G and that's equal to internal energy U plus pressure P times volume V.
Minus temperature T times entropy S. And a constant temperature and pressure
by contrast to the Helmholtz free energy which is volume.
Spontaneous processes occur to minimize G until the system's at equilibrium at
which point only reversible processes for which dG equal 0 occur.
1:01
The maximum non PV work that can be extracted from a spontaneous process
occurring at constant temperature and volume or constant temperature and
pressure is delta A or delta G respectively.
Depending on which of those two conditions holds.
Either isothermal, isochoric is actually how you say constant volume.
So, constant T constant V is isothermal isochoric or isothermal, isobaric, that
is constant temperature, constant pressure.
Those correspond to Helmholtz and Gibbs free energies respectively.
1:37
Spontaneous free energy changes can depend on a balance of energetic and
entropic changes. They can go either way depending on the
temperature. When the temperature causes the entropy
to outweigh an energy or enthalpy preference.
We looked at Maxwell relations and Maxwell relations are determined through
the equality of the mixed partial derivative of thermodynamic state
functions. With respect to other thermodynamic
functions. And so, one example that we derive from
Helmholtz's free energy was that the partial derivative of pressure with
respect to temperature when holding volume constant is equal to the partial
derivative of entropy with respect to volume when holding temperature constant.
2:24
And the reason Maxwell relations are useful is that they can establish a
connection between thermodynamic state functions, which may be tricky to
measure, such as the entropy and PVT equations of state.
So, those are easy quantities to measure pressure, volume and temperature.
And that's what appears everywhere else in this particular Maxwell relation.
2:45
An example of non PV work, which can be extracted from a system is stretching a
rubber band a length delta l against a restoring force f, for example.
So, more work is required at higher temperatures because the entropy of the
rubber band decreases when it's stretched.
3:06
Natural independent variables for a given state function are those, which permit
derivatives of that state function with respect to those variables to be
expressed as simple thermodynamic functions.
For example, the natural independent variables of H are S and P, which leads
to partial derivative H with respect to S at constant pressure equals temperature.
And, the partial derivative of H with respect to pressure at constant entropy
is equal to volume. So, there you see these simple,
thermodynamic variables. The Gibbs free energy of an ideal gas as
a function of temperature and pressure can be related to the pressure and the
standard molar Gibbs free energy at one bar.
Using G over bar at a given temperature and pressure is equal to G superscript 0
at temperature. This is the standard molar Gibbs free
energy at a given temperature and it is defined as the standard molar Gibbs free
energy at 1 bar plus RT log P. So, I only know what pressure I'm going
to in order to know what the new free pressure will be, given a tabulated
standard molar free energy. The temperature dependence of the Gibbs
free energy can be expressed through the Gibbs Helmholtz equation.
And that is the partial derivative with respect to T of G over T, holding
pressure constant is minus H over T squared, the Gibbs-Helmhotz equation.
And then finally, the Gibbs free energy as a function of temperature can also be
assembled from the enthalpy at a given temperature.
Which is evaluated relative to enthalpy at 0 kelvin, by doing measurements of
heat capacities. Minus T times the third law entropy at a
given temperature. And again, that is evaluated from
measurements of heat capacities at various temperatures.
Except what's being integrated is CP over T, instead of just CP, as is true for
enthalpy. So, given those enthalpy and entropy
quantities, we can always determine a free energy.
5:19
All right, those are the key points and hopefully those will be helpful to you as
you address the homework. And we've actually come to the end of
statistical molecular thermodynamics, the eight weeks of this course on Coursera.
So, I appreciate you holding out to the end and I hope you found it enjoyable and
you've learned something along the way. And I also hope you'll indulge me.
Dr. Christopher J. CramerDistinguished McKnight and University Teaching Professor of Chemistry and Chemical Physics
