Thermal properties of bodies in fractal and cantorian physics

The general gas law for real gases in its more applicable form than the widely used laws (e.g. van der Waals, Berthelot, Kammerlingh-Onnes) has been also formulated. The energy density, which is in this case represented by the gas pressure p = f (K, D), can gain generally complex value and represents the behaviour of real (cohesive) gas in interval D ∈ (1,3〉. The gas behaves as the ideal one only for particular values of the fractal dimensions (the energy density is real-valued). Again, it is shown that above the critical temperature (kT > Kℏc) and for fractal dimension Dm > 2.0269 the results are comparable to the kinetics theory of real (ideal) gas (van der Waals equation of state, compressibility factor, Boyle's temperature). For the critical temperature (Kℏc = kTr) the compressibility factor gains Z = 1 (except for the ideal gas case D = 3) also for the fractal dimension D = 1/ϕ = 1.618033989, where ϕ is the golden mean value of the El Naschie's golden mean field theory. To determine the minimum it is also possible to employ the Lambert's W− Function u(A) = A + W[−Aexp(−A)], whereA ≈ 0.6779 and u ≈ −0.7330. The thermal properties of fractal structures (thermal capacity, thermal conductivity, diffusivity) and additional parameters (enthalpy, entropy, etc.) will be defined using the mathematic apparatus in the future. Good agreement of the fractal model with experimental data is documented on the compressibility factor of various gases.