Any object can emit and absorb radiation and the power of emission can be represented by the Stefan-Boltzmann law:

$$P=A\epsilon\sigma T^4$$

In many texts the net power radiated is the difference between the power emitted and the power absorbed:

$$P_{net}=A\epsilon\sigma (T^4-T_s^4)$$

where T_s is the temperature of the surroundings.

Why can the surrounding and the object share the same $\epsilon$ ?

If we try to find out the radiation emitted from the surrounding it should be $P_s=A\epsilon_s\sigma T_s^4$, and if $\epsilon_s<\epsilon$, we will get a strange result that energy radiated from the surrounding is less than the radiation absorbed by the body from the surrounding. What am I missing?

Any object can emit and absorb radiation and the power of emission can be represented by the Stefan-Boltzmann law:

$$P=A\epsilon\sigma T^4$$

In many texts the net power radiated is the difference between the power emitted and the power absorbed:

$$P_{net}=A\epsilon\sigma (T^4-T_s^4)$$

where $$T_{s}$$ is the temperature of the surroundings.

Why can the surrounding and the object share the same $\epsilon$ ?

If we try to find out the radiation emitted from the surrounding it should be $P_s=A\epsilon_s\sigma T_s^4$, and if $\epsilon_s<\epsilon$, we will get a strange result that energy radiated from the surrounding is less than the radiation absorbed by the body from the surrounding. What am I missing?

Any object can emit and absorb radiation and the power of emission can be represented by the Stefan-Boltzmann law: P=AεσT^4

In many texts the net power radiated is the difference between the power emitted and the power absorbed:

Pnet=Aεσ(T^4-Ts^4) where Ts is the temperature of surrounding.

Why the surrounding and the object can share the same ε ?

If we try to find out the radiation emitted from the surrounding it should be Ps=AεsσTs^4, and if εs<ε we will get a strange result that energy radiated from the surrounding is less than the radiation absorbed by the body from the surrounding. How to solve it?

Any object can emit and absorb radiation and the power of emission can be represented by the Stefan-Boltzmann law:

$$P=A\epsilon\sigma T^4$$

In many texts the net power radiated is the difference between the power emitted and the power absorbed:

$$P_{net}=A\epsilon\sigma (T^4-T_s^4)$$

where T_s is the temperature of the surroundings.

Why can the surrounding and the object share the same $\epsilon$ ?

If we try to find out the radiation emitted from the surrounding it should be $P_s=A\epsilon_s\sigma T_s^4$, and if $\epsilon_s<\epsilon$, we will get a strange result that energy radiated from the surrounding is less than the radiation absorbed by the body from the surrounding. What am I missing?