Thermodynamic model for the quantitative description of the electromotive force in a thermocouple has been developed. Thermodynamic
equilibrium was applied to the system of electrons in two metals in a contact, contrary to the consideration of the dynamics
of electrons in a metal under external temperature gradient in the previous classical (Drude) and quantum (Sommerfeld) approaches.
The new model has two parameters, the ‘universal’ sensitivity ɛ0 and the characteristic temperature of a particular thermocouple Θv, and quite simple expression for the emf ΔU=ɛ0(T−Θvln(1+T/Θv) and sensitivity ɛ(T)=ɛ0T/(Θv+T). The model is shown to fit the experimental data very well at low temperatures. At high temperatures, the model is less
The characteristic temperature Θv depends on the difference between the electron heat capacity coefficients γ1−γ2 of two metals in the thermocouple. The greater the difference, the higher the sensitivity of the thermocouple.
Thermodynamic consideration of thermoelectricity in metals was applied to the Peltier effect, like it was done recently for
the Seebeck effect. The Peltier coefficient was derived from the difference in the total energy of electrons in two metals
in contact: Π=ɛ0Tln(1+TΘV), where ɛ0 is the ‘universal’ sensitivity of thermocouples and ΘV is the characteristic temperature of a particular thermocouple.
The Peltier and Seebeck coefficients derived from the new thermodynamic model were shown not to hold the Thomson relation
exactly, but only in the low-temperature limit.
A procedure for measurement of the heat of zeolite dehydration by scanning heating has been designed. Simultaneous data on heat flow (DSC) and mass loss (TG) are required for evaluation. The heating rate depends on the experimental conditions (point-spread function, sample mass, crucible design, and calorimetric reproducibility). Dehydration measurements have three advantages as compared with the sorption procedure: i) one can investigate samples with irreversible dehydration; ii) no approximation model is needed for calculation of the partial molar heat of dehydration; and iii) the procedure is not labor-consuming.The procedure was tested on the natural zeolites heulandite, chabazite and mordenite. The results are close to those measured by the sorption procedure. The partial molar heat of dehydration was found to depend on the water content. It increases from 50 to 87 J mol–1 K–1 for heulandite, from 53 to 81 J mol–1 K–1 for chabazite, and from 51 to 71 J mol–1 K–1 for mordenite.The approximation of the heat of sorption by linear regression was found to be wrong. Detection of a phase transitioN after this approximation has no meaning.
Conventional thermodynamic expression predicts that the isobaric heat capacity decreases with increasing pressure. In model
calculations, heat capacity increases with pressure, decreases, or remains insensitive to pressure, depending on the model
applied. The expression cannot be applied to the gases, but experimental data on gases show evidently that heat capacity increases
Considering the change in enthalpy along two different paths with identical starting and ending points, we derive new expression
dCP/dP=αV, where α is the volume coefficient of thermal expansion and V is the molar volume. The expression predicts the increase in CP with pressure and can be applied to gases. The test of the new expression against accurate literature data on the heat capacity
of air, gaseous and liquid, demonstrates its validity.
Approximation polynomial of temperature for the emf of a thermocouple is of high order, with low accuracy and many digits
in the polynomial coefficients. These disadvantages are shown clearly in comparison with the approximation of high-temperature
heat capacity. The fitting problems result from the fundamental reason, namely, the particular analytical expression for the
emf as the function of temperature.
In the approximation theory, this disadvantage is known as Runge’s phenomenon. In this report, it is shown to be typical of
the functions with a negative power of the variable, where the derivation produces a factorial.
Relation between the calibration coefficient of a DSC sensor k(T) and the sensitivity of a thermocouple e(T) which the sensor is made from was derived from the analysis of a heat transfer inside a DSC cell. Ratio e(T)/k(T) is equal to A+BT3. The first component depends on heat conduction and the second one on radiation. The relationship was tested for DSC-204
Netzsch using (i) data on calibration vs. enthalpies of phase transitions (reference samples) and (ii) measurements of heat capacity of corundum. Both tests show very good agreement between experimental data and predicted theoretical
The melting of PbBr2 in sealed crucibles was investigated by means of DSC. Three factors were considered to affect melting point: i) impurities, ii) the bromine pressure over the PbBr2, and iii) photolysis. Both crystals and powders were investigated. The peak of the melting changed after sample grinding. The bromine pressure over the PbBr2 was found to cause a significant error in the determination of the melting point.Lead bromide melts at 370.6±0.2°C. The heat of melting is 42.9±1.8 J g–1.
Various ways of thermodynamic evaluations can yield different results, contradicting to one another. Such a case is considered a paradox, with the attempts to solve it. This is because thermodynamics is thought to be the science established on solid conceptual ground, with accurate mathematical evaluations. Recently, we faced similar problem, when the relationship between heat capacity and pressure is described by two different equations, predicting opposite behavior. Both equations are free of evident errors. In searching for the reason of the discrepancy, we found out that it is common practice in thermodynamic evaluations to tune the mathematical operations in order to receive the necessary result. It is typical of empirical science, but inappropriate for the fundamental knowledge based on axiomatic background. Short historical survey on experimental data and theoretical concepts dealing with the relation between heat capacity and pressure proves that the thermodynamics is very flexible and effective tool for the solution of the problems in the field of relationships among P–V–T parameters and thermophysical properties of matter. One should not consider the solutions as the universal laws.