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Temperature vs. chemical potential

Zhigang Suo's picture

For the third time I am teaching the graduate course on soft active materials.  This course is called Advanced Elasticity in the Catalog of Courses.  In the last several years, I have dropped several traditional topics, and focused on thermodynamics and finite deformation.  I have added several topics where both thermodynamics and finite deformation play significant roles, such as elastomeric gels and dielectric elastomers.

In the class yesterday, we talked about chemical potential, a quantity I’ll need when talking about gels.  Toward the end of the lecture, I talked about my own experience in teaching temperature and chemical potential.  The students seemed to be amused by the following comparison.

The temperature of a system measures the change in the entropy of the system associated with the change in energy. We measure temperature by using a thermometer, and adding energy to the system by using a heater. Temperature corresponds to the daily experience of hotness. Indeed, our daily experience of hotness is so pervasive that it may even impede our learning of thermodynamics. It takes significant effort for us to sort out, of all our feelings for hotness, what is essential and what is incidental. Only then we can link our daily experience of hotness to the thermodynamics of temperature. See notes on temperature.

The chemical potential of ethanol in a glass of wine measures the change in the entropy of the wine associated with the change in the number of molecules of ethanol, and corresponds to the daily experience of the smell of the wine.

Given similarly pervasive roles of temperature and chemical potential in our lives, we may wonder why we do not have the same level of familiarity with the two types of quantities. I can think of two reasons: one is cultural and the other technical. The cultural reason is that when we felt something was hot, our parents told us that the temperature was high. However, when we smelled a strong wine, our parents missed the teachable moment, and failed to tell us the chemical potential of ethanol was high. The phrase—the chemical potential of ethanol—is simply not in the popular vocabulary. So blame our parents.

The technical reason is that, when we feel that something is hot, we attribute the sense of hotness to a single quantity: temperature. However, when we smell something, we may sense multiple quantities: a list of chemical potentials of a list of species of molecules. It is simpler to deal with one quantity than deal with multiple quantities. So blame our world: it confuses us with too many species of molecules.

Of all species of molecules, water is particularly significant to us. Our parents do tell us about humidity. Indeed, our experience of humidity can be mapped to the thermodynamics of the chemical potential of water, just as our experience of hotness can be mapped to the thermodynamics of temperature.

I’d like to hear about your experience in teaching and learning chemical potential.

Comments

Libb Thims's picture

Sorry to keep posting on your blog, but your posts show up my RSS feed navigator, which I usually check daily or weekly.

Re: "The temperature of a system measures the change in the entropy of the system associated with the change in energy." Where do you keep getting these definitions from? It seems like you are pulling these out of a hat?

Zhigang Suo's picture

For the particular exampe "the wine" in the notes on chemicaal potential, the entropy is a function of energy, volume and the number of water molecules.  The partial derivative of entropy with respect to energy is 1/T.  More detailed development of the idea of temperature is described in the notes on Temperature.

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