Differential Determination
of Heats of Compression:
An Attempt at Direct Determination
of a Third Derivative of G

For the purpose of experimental determination of a third derivative of Gibbs energy, G, we construct a novel apparatus consisting of double cells and a hydraulic pressure device, together with a thermo-module directly determining the difference in heats of compression between the two cells. Each cell contains aqueous solutions with a small mole fraction difference, Δxi. By applying pressure by a hydraulic pump, δp, on both cells, the difference in the heats of compression, Δ(δH) between the two cells is monitored as the output from the thermo-module sandwiched by the two cells. Thus, the quantity, Δ(δH)/(δpΔxi) can be obtained, which is expected to be a good approximation for ∂2H/(∂p∂xi), which is a third derivative proportional to the partial molar thermal expansivity of the i-th component. Preliminary measurements showed some promise.

(by Y. Koga & A. Inaba)

	Fig. 1. Schematic diagram of a double cell pressure perturbation assembly. Each cells with the same volume are filled with an aqueous solutions with a small mole fraction difference, Δxi. A small pressure, δp is applied to both cells concurrently, and the difference in the heats of compression between the two cells, Δ(δH) is determined by the output of a thermo-module sandwiched by the two cells.
	Fig. 2. The output in voltage of thermo-module as a function of time. At every 100 sec., the pressure of both cells changes from high to low and reverses several times. The straight lines drawn are schematic presentation of extrapolation to determine the temperature difference between the two cells induced by pressure perturbation.