Radiation... Emission and Absorption

AlexChandler

1. The problem statement, all variables and given/known data

A sphere of radius 0.500 m, temperature 27.0°C, and emissivity 0.850 is located in an
environment of temperature 77.0°C. At what rate does the sphere (a) emit and (b) absorb
thermal radiation? (c) What is the sphere's net rate of energy exchange?


2. Relevant equations

P_emit=σεAT_object^4
P_absorb=σεAT_environment^4

σ=5.6704 x 10^4 W/(m^2 K^4)=Stefan-Boltzmann constant

3. The attempt at a solution

I am able to use the equations and find the answer that the book is looking for.. but I do not understand the second listed equation. Does this account for only the energy radiated by the molecules in the environment? Will this equation work in any environment...(air/water/concrete...etc)? My book says that this equation gives the energy the object absorbs via thermal radiation. Do we not have to worry about energy transferred by conduction? The collisions between the molecules of the environment and the molecules of the object will tend to transfer energy to the object since its molecules are moving slower on average. How do we account for this energy?
Thank you. I hope I am not horribly mistaken or somehow being stupid.