We can use Stefan-Boltzmann Law, P = 0 AeT“, to produce a very rough estimation of temperature of the Earth. Follow the steps below to estimate the temperature of the Earth. At the radius of the Earth's orbit (1 astronomical unit away from the Sun), the thermal radiation from the Sun has an intensity of about S = 1370 W/m², known as the "solar constant." a. In terms of solar constant S and radius of the Earth R, what is the total solar power (Pin) incident on and absorbed by the Earth? Assume that Earth can be treated like a blackbody and will absorb all radiation incident on it. Hint for (a) Pin = Give your answer in terms of S, R, and other numerical constants (spell out Greek characters, i.e. "pi" for 7). b. As the temperature of the Earth rises, the power emitted by the Earth (Pout) increases. Give an expression for power emitted by the Earth, in terms of its radius and other constants (see some of the constants used in Stefan-Boltzmann Law). Hint for (b) Pout = Give your answer in terms of R, o, and T, T being temperature of the Earth in the Kelvin scale. Assume that e = 1 (the Earth is a perfect blackbody). C. At equilibrium, Pin = Pout Using your results in (a) and (b) and solving for T, find your estimate of Earth's temperature. Give your answer in kelvins. Hint for (c) T = K.

icon
Related questions
Question
We can use Stefan-Boltzmann Law, P = o AeT“, to produce a very rough estimation of temperature of
the Earth. Follow the steps below to estimate the temperature of the Earth.
At the radius of the Earth's orbit (1 astronomical unit away from the Sun), the thermal radiation from the
Sun has an intensity of about S = 1370 W/m², known as the "solar constant."
a. In terms of solar constant S and radius of the Earth R, what is the total solar power (Pin) incident
on and absorbed by the Earth? Assume that Earth can be treated like a blackbody and will absorb all
radiation incident on it.
Hint for (a)
Pin
Give your answer in terms of S, R, and other numerical constants (spell out Greek characters, i.e.
"pi" for T).
b. As the temperature of the Earth rises, the power emitted by the Earth (Pout) increases. Give an
expression for power emitted by the Earth, in terms of its radius and other constants (see some of
the constants used in Stefan-Boltzmann Law).
Hint for (b)
Pout
Give your answer in terms of R, o, and T, T' being temperature of the Earth in the Kelvin scale.
Assume that e = 1 (the Earth is a perfect blackbody).
c. At equilibrium, Pin
Earth's temperature. Give your answer in kelvins.
Pout. Using your results in (a) and (b) and solving for T, find your estimate of
Hint for (c)
T.
К.
Transcribed Image Text:We can use Stefan-Boltzmann Law, P = o AeT“, to produce a very rough estimation of temperature of the Earth. Follow the steps below to estimate the temperature of the Earth. At the radius of the Earth's orbit (1 astronomical unit away from the Sun), the thermal radiation from the Sun has an intensity of about S = 1370 W/m², known as the "solar constant." a. In terms of solar constant S and radius of the Earth R, what is the total solar power (Pin) incident on and absorbed by the Earth? Assume that Earth can be treated like a blackbody and will absorb all radiation incident on it. Hint for (a) Pin Give your answer in terms of S, R, and other numerical constants (spell out Greek characters, i.e. "pi" for T). b. As the temperature of the Earth rises, the power emitted by the Earth (Pout) increases. Give an expression for power emitted by the Earth, in terms of its radius and other constants (see some of the constants used in Stefan-Boltzmann Law). Hint for (b) Pout Give your answer in terms of R, o, and T, T' being temperature of the Earth in the Kelvin scale. Assume that e = 1 (the Earth is a perfect blackbody). c. At equilibrium, Pin Earth's temperature. Give your answer in kelvins. Pout. Using your results in (a) and (b) and solving for T, find your estimate of Hint for (c) T. К.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer