Question

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?

Answer 1

the final temperature is T=305.63 K

Step-by-step 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