# Thermodynamics--Gibbs free energy: what can we actually measure in the lab?

by bzz77
Tags: entropy, gibbs energy, gibbs free energy, thermodynamics
 P: 33 Hi everyone: I am getting back into thermodynamics after a long absence and have realized that there are basics I have never understood. If a patient person could either explain or direct me to an online resource, I'd be very grateful. I have been on Google, but without success. Which thermodynamic potentials (U, A, H, G) can we actually measure directly in the lab (versus calculate)? I'm particularly interested in G. For example, if we consider the expression, G = H - TS, we can't measure entropy (right)? I know that Gibbs Free Energy of Formation values describe the amount of energy that is released or consumed when a phase is created from other phases. Does this mean heat energy? So we measure Gibbs Free Energy of Formation by measuring the amount of heat lost or given out by formation of a phase? How then do we separate out H and TS? Thank you very much.
 Sci Advisor P: 5,444 AFAIK, calorimeters directly measure ΔH (the change in enthalpy), but I have also seen instruments (differential scanning calorimeters) that measure ΔΔG- the change of ΔG as some parameter is varied. Some manufacturers: http://www.microcal.com/products/dsc/default.asp http://www.netzsch-thermal-analysis....g-calorimeter/ http://www.tainstruments.com/product...&n=1&siteid=11
 Sci Advisor P: 3,266 And the voltage of a battery is directly proportional to Delta G. Also S is directly measurable.
P: 789

## Thermodynamics--Gibbs free energy: what can we actually measure in the lab?

 Quote by DrDu And the voltage of a battery is directly proportional to Delta G. Also S is directly measurable.
I assume you meant $\Delta S$. How is $\Delta S$ directly measured?
 P: 33 Thanks everyone. I would also be curious to know how dS is measured. So it sounds like we can't measure G directly.
P: 91
 Quote by bzz77 Thanks everyone. I would also be curious to know how dS is measured. So it sounds like we can't measure G directly.
Yes. Because we must take into account all molecules, atoms, bonds, their physical arrangement in space and so, in order to know its actual internal energy.

As I remember, the reference point for internal energy and entropy was absolute temperature. Therefore to measure the entropy of a system, you should look at the system at -273.15 degree and afterwards measure its ΔS by heating it up. Since ΔS = S_final - S_initial, and since initial entropy is 0, what you measure is actually its exact entropy.

But, it is impossible to cool down a system to absolute temperature. As I know, this is why we cannot measure G directly but can only measure its change.

If I wrong, please let me know :)
 Sci Advisor P: 3,266 It is possible to measure the change in entropy. Just couple the system whose entropy change you want to measure to another process whose entropy change you know. This other process can be used as an entropymeter. You have to scale it so that the combined process is reversible. This is quite a standard argument in theoretical thermodynamics, check e.g. http://arxiv.org/pdf/math-ph/0204007v2.pdf However, in practical applications it is usually easier to determine Delta S from calorimetric data. As far as Delta G is concerned it is the non-volume work a system can do under reversible conditions at constant pressure and temperature. Work is evidently measurable, e.g. electric work done by a battery, as I stated earlier.
P: 789
 Quote by DrDu It is possible to measure the change in entropy. Just couple the system whose entropy change you want to measure to another process whose entropy change you know. This other process can be used as an entropymeter. You have to scale it so that the combined process is reversible. This is quite a standard argument in theoretical thermodynamics, check e.g. http://arxiv.org/pdf/math-ph/0204007v2.pdf However, in practical applications it is usually easier to determine Delta S from calorimetric data. As far as Delta G is concerned it is the non-volume work a system can do under reversible conditions at constant pressure and temperature. Work is evidently measurable, e.g. electric work done by a battery, as I stated earlier.
Doesn't that beg the question? How do you know the entropy of the other system? (I will check the arxiv article)
 P: 789 I looked at the arxiv article, and it looks like a good one, but it is pretty long and dense and the approach is new to me. Can you point out where in the article an "entropymeter" is suggested?
 Sci Advisor P: 3,266 A. Thess has tried to write a more popular compilation of the Lieb Yngvarson approach: http://www.amazon.com/The-Entropy-Pr.../dp/3642133487 I think he calls a machine to measure entropy a Yngvarson Lieb machine.
P: 789
 Quote by DrDu A. Thess has tried to write a more popular compilation of the Lieb Yngvarson approach: http://www.amazon.com/The-Entropy-Pr.../dp/3642133487 I think he calls a machine to measure entropy a Yngvarson Lieb machine.
I'm starting to think these are two excellent articles. I still don't think you can have an entropy meter, but my thinking might be changed after I read and understand these articles. At any rate, they seem to not be buying into the usual junk. They understand that "Classical thermodynamics" is a self-consistent theory that does not make nor does it need to make any connection to statistical mechanics. I like that. I also like that they understand that the zeroth law does not define thermodynamic temperature, its simply an equivalence relationship among equilibrium states. Its going to take me a while to get through them...

By my present understanding, the only thing we can measure is the work extracted from a system, and the work done on the system. Also, we can measure the volume of a system. We can adiabatically isolate a system. (prevent heat flow in and out) We can mechanically isolate a system (prevent it from doing work, or having work done on it), etc. The first law is conservation of energy: there is something called the internal energy of the system. If you do (measureable) work on an adiabatically isolated system, the energy transferred by that work all goes to increase the internal energy by the same amount, and vice versa. So under some conditions, you can measure the change in internal energy. For an adiabatically non-isolated system, the difference between the work and the internal energy is not zero and is called heat. The second law (with the help of the zeroth) says you can define temperature and entropy change such that their product is the heat exchanged. Then, with the help of Carnot engines, etc, temperature can be defined and measured, and so, therefore, can entropy. Lieb et. al. say that all the stuff with Carnot engines is not necessary, and I'm beginning to like their argument. So to address the OP, I'm still thinking about it.
P: 5,462
 Which thermodynamic potentials (U, A, H, G) can we actually measure directly in the lab (versus calculate)? I'm particularly interested in G. For example, if we consider the expression, G = H - TS, we can't measure entropy (right)?
Surely this depends upon you interpretation of measure directly.

For instance I know of no way to measure temperature directly - Temperature is always measured by its physical effect on the 'thermometer'

Secondly lies the issue that you have asked to measure absolute values, without defining base points.

Others have pointed out and conducted a discussion based upon noting that we can measure only changes to these by observing certain quantites input to or extracted from a system (heat, mechanical work, other energies) plus the direct measurement of other system state variables such as volume.

Alternatively we may hold such quantities (volume) fixed as in a bomb calorimeter thus only needing to measure the heat flows.

However even here we run up against the interpretation of the word 'directly'.
Conventionally we don't use a bomb calorimeter to measure directly we use a comparative method - that is we separately measure the quantity of electrical energy to produce the same thermal effects as the process and compare.
This is similar to noting that a beam balance doesn't measure mass directly it compares against a standard, or potentiometric measurements in electricity or.....
P: 789
 Quote by Studiot Surely this depends upon you interpretation of measure directly. For instance I know of no way to measure temperature directly - Temperature is always measured by its physical effect on the 'thermometer' Secondly lies the issue that you have asked to measure absolute values, without defining base points. Otheres have pointed out and conducted a discussion based upon noting that we can measure only changes to these by observing certain quantites input to or extracted from a system (heat, mechanical work, other energies) plus the direct measurement of other system state variables such as volume. Alternatively we may hold such quantities (volume) fixed as in a bomb calorimeter thus only needing to measure the heat flows. However even here we run up against the interpretation of the word 'directly'. Conventionally we don't use a bomb calorimeter to measure directly we use a comparative method - that is we separately measure the quantity of electrical energy to produce the same thermal effects as the process and compare. This is similar to noting that a beam balance doesn't measure mass directly it compares against a standard, or potentiometric measurements in electricity or.....
Right, a thermometer measures its own volume, we can measure the work put into or taken out of a system. Those are direct measurements. What others are there? The other tools we have are the ability to thermally isolate a system - we are able to transform states adiabatically. We can mechanically isolate a system by holding its volume constant. And, of course, we can materially isolate a system, not allow mass to flow in or out.

Isn't every thing else derived using the laws of thermodynamics? If we thermally isolate a system and then do work on it, that work goes completely into its internal energy. If we hold its volume constant as well, then all that work will again go completely into its internal energy, but this time as heat energy. But we cannot measure heat or internal energy, only the work we do on the system, and the ways we have constrained the system.

Still working on that arxiv article, which might be saying entropy can be directly measured, but I still have doubts.
 P: 789 Looking through the Thess paper, I still do not see how entropy is measured directly. The "Lieb-Yngvason machine" is a (valuable) conceptual device, but not an actual machine. On page 85, Thess states: "Moreover, Lieb-Yngvason machines...do not exist in reality. In order to determine the entropy of a simple system with one work coordinate, it is necessary to perform two series of measurements on the system. In the first measurement, one has to determine the heat capacity $C_V=(\partial U/\partial T)_V$ as a function of temperature and volume. In the second measurment, one has to evaluate the thermal equation of state $p(T,V)$. The measurement of $C_V$ is accomplished by supplying a small amount of energy $\Delta U$ to the system while keeping the volume constant and measuring the temperature increase $\Delta T$" So just to measure $C_V(T,V)$ requires a direct measurement of temperature and volume and work. Thess goes on to say that to measure the $p(V,T)$ one must directly measure temperature and pressure: That is, temperature, force and area. And we do not directly measure temperature, but rather infer it from, for example, a volume measurement of mercury in a mercury thermometer. So its back down to directly measuring geometry (volume, area), force and work. These are all mechanical parameters. Mechanical parameters are the only thing you can directly measure, I think. All of the purely thermodynamic parameters (e.g. S, T, U, G...) are measured indirectly.
 P: 5,462 Rap, thank you for your in depth exploration of the OP and subsequent suggestions, it shows some good thinking.
 P: 789 Those two books by Lieb and Yngvason, and by Thess, are two of the best books I've (partially) read on entropy since Arieh Ben-Naim's "A farewell to entropy" and the Jaynes papers.
 Sci Advisor P: 3,266 My personal favourite is still C. Caratheodory's article Untersuchungen über die Grundlagen der Thermodynamik, Mathematische Annalen, Vol. 67, 1909, p. 355–386 which is also available somewhere in an english translation. Very nice is also the book H.A. Buchdahl, The Concepts of Classical Thermodynamics (Cambridge University Press, London, 1966). As far as the problem of measurement of entropy is concerned, I still don't see any problem of principle of measuring entropy (differences). Take in mind that entropy is a state function. Usually it is experimentally easy to perform a process to good approximation quasi-statically. Think e.g. of discharging a battery via a very large resistor. If the resistor is much larger than the internal resistance of the battery, the discharge is nearly quasi-static. You can measure both heat production and temperature in that process and thus entropy. Alternatively you could think of coupling the heat produced into a Carnot engine operating against a reservoir of fixed temperature, e.g. ice at 0 deg Celsius. Then the heat taken up by the reservoir, i.e. the amount of water melted, is directly proportional to the entropy change between initial and final state of the system.
P: 789
 Quote by DrDu As far as the problem of measurement of entropy is concerned, I still don't see any problem of principle of measuring entropy (differences). Take in mind that entropy is a state function. Usually it is experimentally easy to perform a process to good approximation quasi-statically. Think e.g. of discharging a battery via a very large resistor. If the resistor is much larger than the internal resistance of the battery, the discharge is nearly quasi-static. You can measure both heat production and temperature in that process and thus entropy. Alternatively you could think of coupling the heat produced into a Carnot engine operating against a reservoir of fixed temperature, e.g. ice at 0 deg Celsius. Then the heat taken up by the reservoir, i.e. the amount of water melted, is directly proportional to the entropy change between initial and final state of the system.
Well, the question is, what is directly measurable, and I don't see how any non-mechanical thermodynamic parameter is directly measurable. You have to have something linear with ticks or tick marks on it and make a direct comparison and read off a scale. A ruler, a protractor, a clock. Even measuring mass is a geometric thing, use a balance and read an angle of deflection. Force you measure mass and acceleration, and for acceleration you use a ruler and a clock. It's almost like the only directly measurable thing is space and time. I think Lieb and Yngvason's point was that IF you had a machine that answered yes or no as to whether one system was adiabatically accessible from another, you would have an "entropy ruler" by which you could directly measure entropy. No need to impose a quasistatic restriction, or introduce heat or temperature or internal energy. Caratheodory's exposition is vague to me, only because I have not studied it enough, I am sure. As I understand it, his exposition is also based on adiabatic accessibility. Lieb and Yngvason have given me a better grasp of adiabatic accessibility, maybe now I can start to make better sense of Caratheodory. Thanks for that Caratheodory reference, maybe that is where I should begin.

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