Why is the 'TS term' included in the expression for Gibbs free energy?

[wannabegenuin]

Hello.
I'd like to ask a question about meaning of Gibbs free energy.
In undergraduate school, I learned that Gibbs free energy is "available" energy we can extract from system at constant pressure and temperature.
G=H-TS=U+PV-TS
In above expression, however, I can't understand why "TS term" is included.
I think "PV" energy term is necessary for making some space to put the system in the environment.
Fig. 5.1 in textbook (An introduction to thermal physics, V. Schroeder), the author explained as "Some energy, equal to TS, can flow in spontaneously as heat", "The more entropy the system has, the more energy the system can get into the heat".
I didn't understand this sentence at all.
My question is "when system has some entropy, why this receives the heat (=TS) from environment?"
Is there anyone who can explain this clearly?

 

[DrDu]

For a closed system we have
$\delta w^*-PdV=dU-\delta q$,
where $w^*$ is the work excluding volume work.
Now by the second law
$\delta q T\le dS$, whence
$\delta w^*\le dU+PdV-TdS$.
Hence, for constant T and P,
$\delta w^* \le dG$.

 

[Chestermiller]

Hello.
I'd like to ask a question about meaning of Gibbs free energy.
In undergraduate school, I learned that Gibbs free energy is "available" energy we can extract from system at constant pressure and temperature.
G=H-TS=U+PV-TS
In above expression, however, I can't understand why "TS term" is included.
I think "PV" energy term is necessary for making some space to put the system in the environment.
Fig. 5.1 in textbook (An introduction to thermal physics, V. Schroeder), the author explained as "Some energy, equal to TS, can flow in spontaneously as heat", "The more entropy the system has, the more energy the system can get into the heat".
I didn't understand this sentence at all.
My question is "when system has some entropy, why this receives the heat (=TS) from environment?"
Is there anyone who can explain this clearly?

In my judgment (and experience), it doesn't pay to spend much of your valuable time trying to assign physical significance to the Gibbs free energy. It is best to just regard it a defined thermodynamic function that is very convenient to use in solving certain kinds of thermodynamic problems. In particular, it is used very extensively in solving chemical systems involving mixtures of species, where the species in different phases are in thermodynamic equilibrium or where chemical reactions are in equilibrium.

 

[Frank Peters]

In my judgment (and experience), it doesn't pay to spend much of your valuable time trying to assign physical significance to the Gibbs free energy. It is best to just regard it a defined thermodynamic function that is very convenient to use in solving certain kinds of thermodynamic problems.

Not correct. Free energy is physically very real.

Let's consider a battery. In a battery, the chemical reactants are segregated and electron transfer occurs by means of an external circuit.

If we immerse the battery (excluding, of course, the external circuit) in a constant temperature water bath and then measure the work peformed after attaching a load (e.g. light bulb, motor, etc.) to the external circuit, this work is equal to delta G, the free energy change.

But there is also heat given off by the battery, as measured by the water bath, and this heat energy is equal to T*S, where S is the entropy change.

Thus, for the battery, the total energy change is G + T*S.

However, we can also mix the battery reactants and allow them to react directly, i.e. with no external circuit. This can be done by mixing the reactants in a container that is immersed in a contant temperature bath. When we meaasure the heat energy given off by the reaction we find that is equal to the enthalpy, or H. Enthalpy, H, is equal to the total internal energy change of the system. But this H is observed to equal G + T*S.

Thus, by using the battery, we can clearly see that a portion of the available energy, T*S, is not available for the useful work, which is measured by G.

G is the useful work obtainable from a system and T*S is the energy that is wasted.

Note: all the above quantities should have a "delta" symbol in front of them since energy is not absolute and we can only talk about changes in energy.

 

[Chestermiller]

Thanks Frank.

I agree that, for certain situations, like chemical processes carried out at constant temperature and pressure, $\Delta G$ can be interpreted physically as the maximum amount of work attainable (over and above P-V work). However, more generally, for arbitrary situations, the physical interpretation of G is quite elusive.

Chet

 

[Frank Peters]

However, more generally, for arbitrary situations, the physical interpretation of G is quite elusive.

I wonder how much of that is due to the manner in which thermodynamics is presented.

If one examines any textbook or website that attempts to discuss thermodynamics one will find only a thicket of abstruse and often impenetrable equations. Intuitive or illustrative examples from actual practical situations are virtually absent.

Mathematics, of course, is absolutely essential, but too much math without intuition can hinder more than help.

 

[Chestermiller]

I wonder how much of that is due to the manner in which thermodynamics is presented.

If one examines any textbook or website that attempts to discuss thermodynamics one will find only a thicket of abstruse and often impenetrable equations. Intuitive or illustrative examples from actual practical situations are virtually absent.

Mathematics, of course, is absolutely essential, but too much math without intuition can hinder more than help.

Huh? Are you saying that I have no real world experience with applying thermodynamics to practical chemical processes (even using those complicated equations)?

 

[Frank Peters]

Huh? Are you saying that I have no real world experience

No. I was not saying anything at all about you personally.

I was talking in general terms about a possible reason why a lot of people have trouble with thermodynamics. It may be that the subject is presented with too much mathematical derivations and not enough intuitive examples.

 

[Chestermiller]

No. I was not saying anything at all about you personally.

I was talking in general terms about a possible reason why a lot of people have trouble with thermodynamics. It may be that the subject is presented with too much mathematical derivations and not enough intuitive examples.

If you're saying that the subject of Thermodynamics is presented very poorly in thermodynamics textbooks, I very strongly agree. One exception, that I like very much, is Fundamentals of Engineering Thermodynamics by Moran et al.

 

[Frank Peters]

If you're saying that the subject of Thermodynamics is presented very poorly in thermodynamics textbooks

Not necessarily poorly presented.

It just seems to me that most textbooks/websites use exclusively a rigorous mathematical approach without being supplemented by intuitive examples.

The original poster apparently has difficulty in seeing through the mathematical thicket.

 

[DrDu]

I wonder how much of that is due to the manner in which thermodynamics is presented.

If one examines any textbook or website that attempts to discuss thermodynamics one will find only a thicket of abstruse and often impenetrable equations. Intuitive or illustrative examples from actual practical situations are virtually absent.

Mathematics, of course, is absolutely essential, but too much math without intuition can hinder more than help.

I remember the situation when I was learning thermodynamics to be just reversed. As a chemist, I learned thermodynamics from Peter Atkins "Physical Chemistry". Temperature was introduced via gas thermometers and an exact definition was promised to be given in a latter chapter, where, after entropy had been introduced equally sloppily using the preliminary temperature concept, T was finally defined as $T=dU/dS|_V$. Completely circular logic. Most texts still introduce entropy via Carnot's engines. While this may have been an acceptable concept in the 18th century, I find it inacceptable in the 21st one.
I think that in thermodynamics many students start with a wrong feeling of having already intuition for concepts like temperature, energy, but they underestimate the effort to make these concepts precise.