The thermodynamic functions of a system are most often determined by measuring their derivatives against an independent thermodynamic variable. Calorimetry can be easily used to measure the rate of heat evolution of a physiochemical change induced by a known variation of one such variable, when the second is kept constant. This procedure allows direct measurements of the most important thermodynamic derivatives.
Temperature-controlled scanning calorimeters (TCSC), in which temperature is taken as the inducing variable and varied as a linear function of time, are the best known instrument of this type and allow measurements of<nobr> (</nobr><nobr /><nobr /><nobr /><nobr /><nobr>H/ </nobr><nobr>T)P or ( </nobr><nobr /><nobr>U/</nobr><nobr /><nobr>T)V.</nobr>Pressure-controlled scanning calorimeters (PCSC) in which pressure is the inducing variable and is varied as a linear function of time are examples of isothermal scanning calorimeters allowing measurements of <nobr>(</nobr> S/ P)T. Calibration of the pump piston displacement as a measure of the volume change inside the cell enables volume to be used as the inducing variable under isothermal conditions so as to construct a volume-controlled scanning calorimeter (VCSC) to measure (<nobr> </nobr><nobr>S/ </nobr><nobr>V)T.</nobr>
The three techniques all involve closed systems; any change in the composition results from perturbation of the thermodynamic state by a variation of the inducing independent variable. The possibility of controlling the three most important thermodynamic variables (P,V,T) in calorimetric measurements allows to realize simultaneous measurements of changes or rates of thermal and mechanical contributions to the thermodynamic potential change caused by the perturbation. For example, simultaneous recording of both heat flow and volume changes resulting from a given pressure change under isothermal conditions (PCSC) leads to simultaneous determination of both (<nobr /><nobr>S/</nobr><nobr /><nobr>P)T and (</nobr><nobr>V/</nobr><nobr /><nobr>P)T</nobr> (or isobaric thermal expansively and isothermal compressibility) as a function of pressure at a given temperature. In the case of the perturbation of the system by a temperature change under isobaric conditions (TCSC), the simultaneous recording of both the heat flow and volume changes used to keep the pressure constant leads to the simultaneous determination of both cP and (V/T)P as a function of temperature at a given pressure. An example is given in figure 1. The technique described above is called transitiometry. In figure 2 a thermodynamic scheme with possible measurements of a PVT-controlled scanning calorimeter is given. In figure 3 a picture of the transitiometer is shown.
Fig 1: Isobaric fusion of urea at 100 bar inducted by linear temperature variation
Fig 2: A thermodynamic scheme of a PVT-controlled scanning calorimeter
Fig. 3: Picture of the Transitiometer
The transitiometer is build for the determination of thermal and mechanical effects of state or phase changes in the pressure range up to 2000 bar and in the temperature range between 20 and 400 °C. Because the transitiometer is made out of Hastelloy C22 also. Systems with corrosive components can be investigated. The data acquisition and process control is done with Labview software. Figure 4 shows a diagram of the transitiometer.
Fig. 4: Scheme of the Transitiometer
Typical scanning rates for the temperature are 1-2 mK / s-1. These low rates allow measurements near equilibrium for many processes. Once the sample is loaded into the experimental vessel, the phenomenon under investigation can be observed in various thermodynamic planes. 500 thermoelements connected in series care for a sensitive output signal. The piston pump has a resolution of 5.683·10-6 cm³/step and a piston volume of 10 cm³. The pressure detectors have a sensitivity of 0.4 mbar. The advantage of this apparatus is the possibility to analyze effects of state or phase changes under pressure. So it is possible to investigate many processes:
Crystallization behavior from pure substances or mixtures under mechanical or gas pressure (CO2, He)
Heats of fusion
Heats of vaporization
Heats of reaction
Heats of sorption