Question

Do not solve the following question numerically unless specifically asked to do so. The flux from the Sun’s surface is given by L(sun)= 4πR(sun)^2 σT(sun)^4 , where T(sun) is the temperature on the Sun’s surface.

(a) What Is the incident luminosity from the Sun seen on Earth’s surface?

(b) Only a part of the luminosity incident on Earth’s surface is reflected back. The fraction of radiation reflected from Earth’s surface, or albedo, is given by A. The other part is absorbed and converted into heat, which is then emitted as thermal emission from the planet. Write an expression for the luminosity absorbed by Earth and the luminosity emitted by Earth. Assume Earth has had ample time to come up to thermal equilibrium. Use the symbol Tsurf to represent the surface temperature of Earth.

(c) Find an expression for the surface temperature of Earth, when the Earth is at thermal equilibrium. Note that thermal equilibrium means that the amount of radiation absorbed by Earth is the same as the amount of radiation emitted by Earth.

(d) Calculate the surface temperature for Earth if A=0.36. If Earth’s observed maximum temperature is 310 K, does the calculated temperature predict an accurate surface temperature? Explain.

(e) Repeat the calculation to find the surface temperature of Venus (A = 0.76). Venus has an observed maximum temperature of 750 K. Is the calculated surface temperature for Venus accurate? Why or why not?

Answer 1