Atkins' 4 Laws that Drive the Universe: Chapter 4 notes

Chapter 4 is a discussion of free energy.

In this chapters, Atkins develops a more detailed definition or criterion fir spontaneity.  Starting with the second law requiring an increase in the entropy of the universe for spontaneous proceses,  he begins the discussion by finding an equation for the change in the entropy of universe using properties og the system only and arrives at a bookkeeping property called the Helmholtz energy.

Later, he states this:

"...provided we limit our attention to processes at constant temperature and volume, spontaneous changes correspond to a decrease in Helmholtz energy of the sytem.  The restrictions of the conditions of constant volume and temperature has allowed us to express spontaneity solely in terms of the properties of the system: its internal energy, temperature, and entropy."

A succinct but profound statement encapsulating the idea that the ability of a system to undergo spontaneous change ( and therefore do work) is dependent on its current state of internal energy, temperature, and entropy.

Further on, he warns against a faulty interpretation of decreasing Helmholtz energy as equivalent to increasing universe entropy.  One might be tempted to think that spontaneity stems from the system's tendency to lower its internal energy and raise its entropy.  He noted that this is simply a by-product of the need for the surrounding's entropy to increase and that spontaneity's sole requirement is still an increasing entropy for the universe.

Excellent molecular description of the Helmholtz energy property, A also called the work function.  First dA = dU - TdS.  TdS is the heat transferred to surroundings in a reversible process (Clausius equation).  Subtracting this term from dU leaves behind the energy that can be used to do work at constant T.  From a molecular point of view, A = U - TS, TS represents the amount of energy due to disorderly motion of molecules corrresponding to energy that can be transferred as heat.  What is left after subtracting this from U is A, energy due to ordered motion of molecules and thus can be used for work.

On TdS being either a tax or a tax refund:

"...TdS is a tax that the surroundings demand from the system to compensate for the reduction in entropy of the system, and only dU-TdS is left for the system to pay out as work."

If the entropy of the system increases, then heat can flow from the surroundings to the system even though it results in a decrease innthe entropy of the surrounding.  In this case, TdS becomes a tax refund.  dA is greater than dU because TdS is added to dU (TdS is a negative in this case).

On Gibbs Free Energy:

G = A + pV (takes into account expansion work that may need to happen)

A = U - TS (constant T and V)

H = U + pV (constant pressure)

Therefore,

G = H - TS

A is a fundamental property that can be defined by a molecular description.  G is a bookkeeping or accounting term.

Leads to the following criteria for free energy changes (both negative) under two different conditions:

"at constant volume, a process is spontaneous if it corresponds to a decrease in Helmholtz energy.

at constant pressure, a process is spontaneous if it corresponds to a decrease in Gibbs energy"

In bioenergetics, the change in Gibbs free energy is the useful one as most biochemical processes occur at approximately constant T and P.