To determine the net rate of radiation heat transfer in this system, we can use the Stefan-Boltzmann law. The net rate of heat transfer between the two surfaces is given by Q = εσA(T1^4 - T2^4), where Q is the net rate of heat transfer, ε is the emissivity of the surface, σ is the Stefan-Boltzmann constant, A is the surface area, T1 is the temperature of the hotter surface, and T2 is the temperature of the colder surface.
To determine the net rate of radiation heat transfer between the two surfaces, we can use the Stefan-Boltzmann law. The formula for the net rate of radiation heat transfer is given by Q = εσA(T1^4 - T2^4), where Q is the net rate of heat transfer, ε is the emissivity of the surface, σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4), A is the surface area, T1 is the temperature of the hotter surface, and T2 is the temperature of the colder surface.
For the net rate of radiation heat transfer between the two rectangular surfaces, we can calculate it using the formula mentioned above. The horizontal surface has an emissivity of 0.75, a surface area of 0.8 m², and a temperature of 400 K. The vertical surface is black, so its emissivity is 1, has a surface area of 1.2 m², and a temperature of 550 K.
For the net rate of radiation heat transfer between the horizontal surface and the surroundings, we can use the same formula, but now the temperature difference is between the horizontal surface and the surrounding surfaces. The surrounding surfaces have a temperature of 290 K and an emissivity of 0.85.