The combination of water and CO2 molecules in the atmosphere account for approximately 155 W/m^2 in greenhouse heating.

1. If we start with a black body at 255 K and add 150 W/m^2 in energy flux out of the body, what is the new predicted temperature?

the final temperature is T=305.63 K

Explanation:

using the Stephan-Boltzmann equation for black bodies

q = σ * (T⁴-T₀⁴)

where

q = heat flux = 155 W/m²+150 W/m² = 255 W/m²

σ = Stephan-Boltzmann constant = 5.67*10⁻⁸ W/m²K⁴

T = absolute temperature

T₀ = absolute initial temperature = 255 K

solving for T

q = σ * (T⁴-T₀⁴)

T = (q/σ + T₀⁴) ^ (1/4)

replacing values

T = (q/σ + T₀⁴) ^ (1/4) = (255 W/m² / (5.67*10⁻⁸ W/m²K⁴) + (255 K) ⁴) ^ (1/4) = 305.63 K

T=305.63 K

thus the final temperature is T=305.63 K