The study of radiation exergy has important significance for solar energy and high-temperature engineering. In this paper, several exergy expressions of blackbody radiation were discussed and the differences between Petela's expression of exergy and two other expressions were analyzed. Considering that radiant energy and thermal energy are different, the radiation machine model was established; furthermore, the validity of Petela's formula was indicated by this model. Based on the concept of radiation equivalent temperature, the integral form expression of monochromatic photon exergy was put forward by establishing the infinite-staged Carnot heat engine model. At the same time, an approximate relation between equivalent temperature and radiation wavelength was given. The error of this relation is negligible when calculating the exergy of blackbody radiation within the temperature range of the engineering field. Finally, the monochromatic photon entropy was discussed by considering the infinite-staged Carnot heat engine model, and an expression of photon entropy with integral form was given. The monochromatic photon entropy and exergy proposed in our paper satisfy the thermodynamic relation and can reflect the differences between radiant energy and thermal energy.