Black Body Radiation

A body which emits the maximum quantity of heat for its absolute temperature is termed as a black body. The radiant heat transfer rate from a black body to its surrounds can be stated by the equation shown below.

Q = σAT⁴

Here:

Q = heat transfer rate (Btu/hr)

σ = Stefan-Boltzman constant (0.174 Btu/hr-ft²-°R4)

A = surface area (ft²)

T = temperature (°R)

The two black bodies which radiate toward each other consist of a total heat flux among them. The total flow rate of heat among them is given by an adaptation of equation shown above.

Q = σA(T₁⁴ -  T₂⁴ )

Here:

A = surface area of the first body (ft²)

T₁ = temperature of the first body (°R)

T₂ = temperature of the second body (°R)

All the bodies above absolute zero temperature radiate little heat. The sun and earth both radiate heat to each other. This appears to violate the Second Law of Thermodynamics that states that heat cannot flow from a cold body to a hot body. The paradox is solved by the fact that each body should be in direct line of sight of the other to obtain radiation from it. Hence, whenever the cool body is radiating heat to the hot body, the hot body should also be radiating heat to the cool body. As the hot body radiates more heat (due to its higher temperature) than the cold body, the total flow of heat is from hot to cold, and the second law is still pleased.