Question

Question 13.

A. What is the difference in spectral radiance of the Earth and the sun, respectively, at a wavelength of 4.0 x 10^-12 µm, assuming both Earth and sun are black body emitters? Be careful with your units – you may have to convert. Show your work. [3 pts]

B. As stated earlier, the area under the Planck curve is total radiance. In calculus, calculating the area under the curve is accomplished by calculating an integral of the function. Fortunately, this has already been done by some wonderful physicists in the past, resulting in the following, relatively simple calculation, known as the Stefan-Boltzmann Equation:

  

where M is total emittance (in Wm²), σ is the Stefan-Boltzmann constant (see table above) and T is temperature (in K).

-How much total radiation does the sun (T ≈ 5800 K) emit? [2 pts]

-How much total radiation does the Earth (T ≈ 300 K) emit? [2 pts]

Answer 1

Since the surface area of the sun is larger than the earth the total radiation coming out of the sun will be larger than that of the earth.The radius of sun is about 110 times of earth hence the total radiance will be about 12100 times that of earth.

Since both are black bodies emissivity=1

total radiation of sun=sigma(area)(T^4)

sigma=5.67*10^-8

T=5800K

Area=4pi(R^2)

R=6400*110*1000m

total radiation of earth=sigma(area)(T^4)

sigma=5.67*10^-8

T=300K

Area=4pi(R^2)

R=6400*1000m

Substituting values answer can be easily obtained