Taking the Earth’s temperature. The Stefan-Boltzmann law, relates the transfer r

Question

Taking the Earth’s temperature. The Stefan-Boltzmann law, relates the transfer rate of electromagnetic radiation of a body (called black-body radiation) to its temperature, P = (5.67 × 10^8 W M^2 K^4 )T^4.

(a) If the incoming solar power hitting the earth is P = 342 W m^2 , what would you predict should be the Earth’s temperature?

(b) Now, turn this argument around. The Earth’s actual average temperature is T = 288 K or +15C. Use the SB law to compute the power of radiated from the Earth’s core.

Please Show Steps, Thank You!

Explanation / Answer

a)

P = (5.67 × 10^8 W M^2 K^4 )T^4

342 = (5.67*10^8)*(T^4)

Solve for T

T = (342/((5.67*10^8)))^(1/4) = 278.683182 K

T = 278.683182 = 5.68 °C

B)

T = 288 K

then

P = (5.67 × 10^8 W M^2 K^4 )T^4.

P = (5.67*10^8)*(288)^4

P = 390.0793 W/m2

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