In this problem you are going to calculate what the temperature on Earth would b

Question

In this problem you are going to calculate what the temperature on Earth would be if it had no atmosphere at all. Basically, the planet receives energy (light) from the Sun and then re-radiates that energy back into space. The energy Earth receives every second depends on the Sun's luminosity and the distance between Earth and the Sun. This energy rate is L = 1.73 x 10^17 W. Take this value and use it in the Stefan-Boltzmann formula to determine temperature. How does your calculated temperature compare to the actual average global temperature on Earth: 288 K? What accounts for the difference?

Explanation / Answer

Here L = 1.73 x 1017 W

Here L/A = T4  

where = 5.670367 ×108 Wm2K4

A = area of the earth (if we assume it is sphere) = 4/3 r3 where r = radius of earth = 6,371 km

L/A = T4  

so T4 = 1.73 X 1017 / [4 * * (6371 *1000)2 * 5.670367×108]

T = 279 K

the difference between the formula temperature and actual temperature is due to the emissivity with greenhouse effect (weighted more in the longer wavelengths where the Earth radiates) is reduced more than the absorptivity (weighted more in the shorter wavelengths of the Sun's radiation) is reduced, the equilibrium temperature is higher than the simple black-body calculation estimates. As a result, the Earth's actual average surface temperature is about 288 K.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.