Measuring the partial entropy

Like the free energy, the chemical potential can be separated into a contribution from enthalpy H and another contribution from entropy S the relationship is 

The Maxwell relations of thermodynamics relate quantities formed by differentiating G once with respect to one variable and once with respect to another (Huang, 1987). Choosing the two variables to be T and n leads to the following relationship  

Since E is proportional to p by Eqn (7.2), dSjdn can be measured from changes in E with temperature. Such measurements as a function of x are slow because the temperature must be cycled at each value of x, and they are plagued by thermoelectric voltages generated in the cells (Dahn and Haering, 1983). 

An alternate method that works at constant temperature, but requires more sophisticated equipment, is a calorimetric measurement. A calorimeter measures the heat Q that flows into an electrochemical cell as the cell is discharged or charged. The heat is related to the change in energy S of the intercalation compound and the work done on the cell, leading to the following relationship (Dahn et ai, 1985)  

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