Please help me understand this by showing work. Thank you for your time. A) Assu
ID: 230874 • Letter: P
Question
Please help me understand this by showing work. Thank you for your time.
A) Assuming that the temperatures of the Earth and Sun are constant and in balance, then Ein = Eout. Because we know the value of Ein from the Sun to Earth, we therefore know the amount of energy being emitted from Earth (Eout). The Stefan-Boltzmann equation enables us to calculate the temperature of the Earth based on the energy emitted. Calculate the temperature in degrees Celsius using the value from question 2 and the equation: E = sT4 or T = (E/s)0.25 where s = Stefan-Boltzmann constant = 5.67x10-8 W/m2/K4
B) How well does your simple climate model perform? Is the calculated temperature of the Earth higher or lower than the actual temperature (you might need to search the Web for “average Earth temperature”)? What’s missing from the model that’s important for controlling temperature?
Explanation / Answer
Radiation Laws
All objects emit radiation. The total radiant energy is a function of the object’s temperature. The Stefan-Boltzman Law tells us exactly how much energy is emitted per unit area:
E = sT4
In this equation, T is temperature (in Kelvin) and s is the Stefan-Boltzman constant (5.67e-8 Wm-2K-4). Note that E is an energy flux and has units of Wm-2.
T=(E/s)*0.25
=(390/5.67e-8)*0.25
=104152352.5 kelvin
T=104152079.35 Celsius
B).The average temperature on Earth is about 61 degrees F (16 C). But temperatures vary greatly around the world depending on the time of year, ocean and wind currents and weather conditions. Summers tend to be warmer and winters colder. Also, temperatures tend to be higher near the equator and lower near the poles.