A planet\'s temperature can be estimated by balancing the energy received and em

Question

A planet's temperature can be estimated by balancing the energy received and emitted. The planet is constantly receiving energy from the Sun, and it reradiates the energy as blackbody radiation, following the Stefan-Boltzmann Law: E = sigma T^4 Where E is the emissive power (Energy per unit time per unit area) [Watts/meter^2]: sigma is the Stefan-Boltzmann constant, equal to 5.67 times 10^-8 [Watts/meter^2/Kelvin^4]: and T is the temperature of the planet [Kelvin]. Balancing the energy absorbed from sunlight with this blackbody radiation allows us to solve for the temperature of a planet. The Earth absorbs only a portion of the energy it receives from the Sun due to its albedo, which describes the fraction of the light reflected by a planet Earth's average albedo is 0.36. A) [Optional for 2060] The total luminosity of the Sun is 3.84 times 10^26 W, while the distance from the Sun to Earth is 1 AU (astronomical unit): 1.496 times 10^11 m. Show that, averaged over the Earth's surface, sunlight provides a flux of about 341 W/m^2. B) Determine the temperature of Earth from the information given in the intro and in part A.

Explanation / Answer

According to Stefan Boltzman law, the effective temperature of the planet is given by

T = {((1-) Isc ) / 4}1/4

where, is the albedo , = 0.36

Isc is the Solar constant, Isc = 1.361 kW/m2 = 1361 W/m2

   is the Stefan Boltzman constant , = 5.67 X 10-8 W/m2/K4

therefore, T= [(1361(1-0.36)) / 4 X 5.67 X10-8] 1/4

  = 253.7 Kelvins = -19.5oC ( because Tcelsius = Tkelvin - 273.15)

Answer T = -19.5oC   

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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