| In this paper, we considered some of the relations of thermodynamical potentials in Tsallils nonextensive formula, using the conception of physical temperature and physical pressure, which is considered by Abe. Then the conception of generalized Gibbs free energy and generalized enthalpy is proformed, by considering the traditional thermodynamical relations. And the relation between the heat capacity in constant pressure and that in constant volume is also changed, because of the difference between the temperature and the inverse of Lagrange multiplier.Next, we considered the heat capacity of the gases of two-atom molecule in nonextensive statistics and compared it with the experiment. We fond that the gases appear extensive ( the parameter q = 1) at normal temperature; while they appear nonextensive ( the parameter q is deflected away from unit ) at low temperature. We supposed that the kinetic energy of the gas molecule is much smaller at low temperature, as compared with potential energy, so the nonextensive effect produced by the long-range interactions of inter-particle becomes important at low temperature. We also fond that the heat capacity of the gases is not only related by the degree of the freedom, but also by the nonextensive parameter q . As an example, we caculated the heat capacity of the many-atom molecule gas.We also studied the two-parameter (κ, r ) generalized statistics, which is proformed considered by Kaniadakis. This new kind statistics contained many kinds of one-parameter statistics, and we mainly considered the physical meaning of the parameterκand r . The temperature gradient T/(?) T, the external force F and the gradient normalization coefficient A/(?) A must stay in the same plane, and their magnitude relation is just defined by r ,κ. As two examples, when the two-parameter statistics returned to the Tsallis andκstatistics respectively, the result was just the one we got before.
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