For the first time we have derived an equation for the temperature (T) dependent work function (W(T)) containing terms up to fifth power of T which gives a modified Richardson-Dushman (MRDE) equation that fits excellently well the experimental data of thermionic current density, J vs temperature, T data for suspended monolayer graphene. It provides a unique technique for accurate determination of work function, W0, Fermi energy, EF0 at 0 K and surface density of charge carriers, ns of graphene. The corresponding values obtained for monolayer suspended graphene are: W0 = 4.592 ± 0.002 eV, EF0 = 0.203 ± 0.002 eV; ns = 3.16x1012 cm-2. The model gives us unique method of determination of the Fermi energy of graphene as a function of temperature. The values of thermal expansion coefficient, α and surface density of charge, ns obtained with the use of the model are in excellent agreement with experiments. We also find that the model explains fairly well the J vs T data for carbon nanotubes, which is reported in a separate paper.