Microcomputer-aided optimal selection of control input for the precision water bath of a heat exchange calorimeter

In heat exchange calorimetry, sample and reference vessels are fixed differentially in a water bath. The heat evolved in the sample vessel is exchanged freely with the ambient water. The accuracy and precision of the calorimetry depend on the temperature range of the drift and fluctuation in the bath water. In the present report, a simple temperature-control system with no empirical factors is proposed for the precision water bath. The heat exchange between the inside of the vessels and the ambient water is expressed by a differential equation or a Newtonian cooling equation. Similarly, the thermal behaviour of a water bath placed in a non-air-conditioned laboratory was also considered to be expressed by the same equation. The heat exchanged with the surroundings, the non-stationary heat flow from warm stirrer motors, and other thermal factors were considered to be part of the heat sources. Cooling water about 2°C lower than the set temperature was circulated in the water bath. The difference between the set temperature and the observed temperature was fed into a microcomputer every second. The latest four data points were used to fit a modified Newtonian equation by the common method of least-squares. The control input to the bath was calculated and given to the heater circuit after power amplification. The program written in basic was about 3.3 kbyte. The controlled range of drift and fluctuation was almost the same, or better, as that previously reported.