If an object absorbs energy at the same rate as it gives off energy, then .

The temperature remains constant

Explanation:

From the radiation law, the net energy radiated P = Power radiated - Power absorbed

Now, let the body be at a temperature T₁ above its surroundings, the rate at which energy is given of is  P₁ = σεAT₁⁴

let T₂ be the temperature of its surroundings, the rate at which energy is absorbed is P₂ = σεAT₂⁴

The net energy radiated (Power radiated) P = P₂ - P₁ = σεAT₂⁴ - σεAT₁⁴ = σεA(T₂⁴ - T₁⁴)

Now, if the object absorbs energy at the same rate it gives off energy, P₁ = P₂ and P = 0.

So, σεA(T₂⁴ - T₁⁴) = 0

Since σεA ≠ 0 then (T₂⁴ - T₁⁴) = 0 ⇒ T₂ = T₁

Since there is no temperature difference, the temperature of the object remains constant.

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