When an object is in radiative equilibrium with its environment at temperature T, the rates at which it emits and absorbs radiant energy must be equal. Each is given by dQ₀/dt = εσT⁴A. If the object’s temperature is raised to T₁ > T, show that to first order in ΔT = T₁−T, the object loses energy to its environment at a rate dQ/dt = 4εσΔTT³A.