Photon statistics in the processes of entropy and the free energy transfer by electromagnetic field in the atmosphere are discussed in this paper. It is shown that multi-equilibrium (generalized Plank's statistics) photon number distribution for monochromatic radiation is due to minimum free energy of the field. A method for simulating free energy fluxes in the atmosphere and free energy balance at its upper boundary is developed, using outgoing thermal radiation and reflected solar radiation. The presence of an extremum in the free energy import to the planet is shown within the model of gray atmosphere under the condition of the energy balance at its upper boundary. The extremum is caused by the optical depth τ of the planet atmosphere and is realizable at τ value, close to a current value for the Earth atmosphere. The assessed annual mean flux of the free energy imported by the Earth is about 59.13 W/m2 or 3 × 1016 W/m2 over the globe. This magnitude determines an integral power of the heat engine of our planet, while its ratio to the power of incoming solar radiation can be considered as the efficiency of this heat engine. Simultaneous satellite monitoring of radiation balance and free energy balance at the upper boundary of the atmosphere could be used to monitor possible variations of integral power of the Earth heat engine and global warming process.