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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.

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