The universal unitary principle of logic test is used to test the mathematical reasoning of pressure equation of ideal gas, and a negative conclusion is given. The study found that, the classical molecular kinetic theory establishes a physical model of the uniform motion of a molecule under the action of an equivalent constant force, which violates the principle of mechanics, and the classical equations for the pressure and temperature of ideal gas derived from such a model are all incorrect. Here we set up a variety of physical models of molecular interaction in accordance with the principle of mechanics, and consistently derive the modified equation of ideal gas pressure. It is proved that the pressure of ideal gas is equal to the molecular energy in unit volume, and the thermodynamic temperature of ideal gas is equal to the quotient of molecular average kinetic energy and Boltzmann constant. Reasoning accords with the unitary principle. The inferences of these different models accords with the unitary principle. Furthermore, the problem of the definite solution of the gas molecular velocity distribution function satisfying the limit condition of light speed is proposed. Finally, the experimental suggestion to verify the theoretical gas temperature correction equation is given.