The cubic equation of state (EoS) is widely applied for modeling fluid thermodynamic properties in chemical processes. However, in the absence of a distinguishable reference property, the supercritical extrapolation of its only temperature-dependent parameter, the alpha function, resulted in nonphysical prediction of supercritical virial coefficients and heat capacities. From a theoretical perspective, we here rigorously derive the universal temperature-dependent behavior of the alpha function, using the generalized van der Waals theory without specifying the interaction potential. To isolate the behavior of the alpha function from the EoS structure, we examine the thermodynamic functions of realistic fluids at low densities. Our study reveals that the alpha function is finite, positive, and monotonically decreases with increasing temperature. We present a set of thermodynamic requirements and accordingly revise the predictive Soave and Twu alpha functions for the Redlich-Kwong and Peng-Robinson EoSs. Our study shows that the revised alpha functions avoid the divergent virial coefficients at infinite temperature, and the nonphysical bump on the heat capacity isobars immediately above the critical temperature, demonstrating the imperative need for thermodynamic requirements for the temperature dependence of the alpha function. Joule-Thomson inversion curve and vapor-liquid equilibria are also investigated. (C) 2018 Elsevier Ltd. All rights reserved.