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- Author or Editor: V. Drebushchak x
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Approximation of the emf of a thermocouple
Part I. The polynomials of temperature and Runge’s phenomenon
Abstract
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.
Abstract
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.
Abstract
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 with pressure. Considering the change in enthalpy along two different paths with identical starting and ending points, we derive new expression dC P/dP=αV, where α is the volume coefficient of thermal expansion and V is the molar volume. The expression predicts the increase in C P 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.
Calibration coefficient of a heat flow DSC
Part III. Electromotive force of a thermocouple as a function of temperature
Abstract
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)=ɛ0 T/(Θv+T). The model is shown to fit the experimental data very well at low temperatures. At high temperatures, the model is less accurate. 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.
Abstract
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+BT 3. 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 function.
Abstract
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=ɛ0 Tln(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.
Abstract
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.
