Suitable model for the calculation of the correlation between the real and the average specific heat capacity and possibilities of its application
Starting from the definition of the average specific heat capacity for chosen temperature range, the analytic dependence between the real and the mean specific heat capacities is obtained using differential and integral calculation. The obtained relation in differential form for the defined temperat...
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Veröffentlicht in: | Hemijska industrija 2013, Vol.67 (3), p.495-511 |
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Sprache: | eng |
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Zusammenfassung: | Starting from the definition of the average specific heat capacity for chosen
temperature range, the analytic dependence between the real and the mean
specific heat capacities is obtained using differential and integral
calculation. The obtained relation in differential form for the defined
temperature range allows for the problem to be solved directly, without any
special restrictions on its use. Using the obtained relation, a general model
in the form of a polynomial of arbitrary degree in the function of
temperature was derived, which has more suitable and faster practical
application and is more general in character than the existing model. New
graphical method for solving the problem is obtained based on differential
geometry and using the derived equation. This may also have practical
significance since many problems in thermodynamics are solved analytically
and graphically. This result was used in order to obtain the amount of
specific heat exchanged using an analytical model or a planimetric method. In
addition, this graphical solution was used for the construction of the
diagram showing the dependence between the specific heat exchanged and
temperature. This diagram also gives a simple graphical procedure for the
calculation of the real and the average specific heat capacity for arbitrary
temperature or temperature interval. The confirmation for all graphic
constructions is obtained using the differential properties between
thermodynamic units. In order for the graphical solutions presented to be
applicable in practice, suitable ratio coefficients have been determined for
all cases. Verification of the model presented, as well as the possibilities
of its application, were given using several characteristic examples of
semi-ideal and real gas. Apart from linear and non-linear functions in the
form of polynomials, the exponential function of the dependence between
specific heat capacities and temperature was also analysed in this process.
nema |
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ISSN: | 0367-598X 2217-7426 |
DOI: | 10.2298/HEMIND111104092P |