How Does a 10% Reduction in Sun's Power Affect Earth's Temperature?

[aforce20]

Homework Statement

1. If the Sun’s power is reduced by 10%, what would the temperature of the Earth be? Assume an albedo of 0.3 and do not consider greenhouse effects.

Homework Equations

There is an equation here in the book but it makes no sense to me

The Attempt at a Solution

Without the understanding of the equation, I have no attempt

 

[tiny-tim]

There is an equation here in the book but it makes no sense to me
…
Without the understanding of the equation, I have no attempt

Hi aforce20!

What equation?

 

[aforce20]

Here is the example from the book that we are supposed to go off of
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The total energy absorbed for a solar constant, or available power per unit area at Earth's orbit, of 1.35 kW/m² is, assuming an albedo (reflectivity) of 30%

P_absorbed = (1 -0.3)( 1.35 kW/m²) ([PLAIN][PLAIN]http://www.kartones.net/images_posts/pi_symbol.png R_E²)

A body at absolute temperature T radiates according to the Stefan-Boltzmann law as

P_radiated = ( 5.67 x 10^-8 W/m² K⁴) T⁴ (4[PLAIN][PLAIN]http://www.kartones.net/images_posts/pi_symbol.png R_E²)

where Earths total spherical surgace area is 4[PLAIN][PLAIN]http://www.kartones.net/images_posts/pi_symbol.png R_E² . Thus, since in the long term the power absorbed must again be radiated for Earth to be in equilibrium, P_radiated = P_absorbed , and [PLAIN][PLAIN]http://www.kartones.net/images_posts/pi_symbol.png R_E² is a common factor , so( 1 - 0.3 ) ( 1.35 kW/m²) = 4(5.67 x 10^-8 W/m²k⁴) T⁴

Therefore,

T⁴ = ( 0.7) (1350 W/m²)/4(5.67 x 10^-8 W/m² K⁴) = 4.17 x 10⁹ K⁴

or

T=254 K

BTW I could not find the pi symbol so I used one from google, that is why it is so huge. Also, this class is for non-science majors so try not go get to technical here.

Thanks

 

[tiny-tim]

The total energy absorbed for a solar constant, or available power per unit area at Earth's orbit, of 1.35 kW/m² is, assuming an albedo (reflectivity) of 30%

P_absorbed = (1 -0.3)( 1.35 kW/m²) (π R_E²)

A body at absolute temperature T radiates according to the Stefan-Boltzmann law as

P_radiated = ( 5.67 x 10^-8 W/m² K⁴) T⁴ (4π R_E²)

where Earths total spherical surgace area is 4π R_E² . Thus, since in the long term the power absorbed must again be radiated for Earth to be in equilibrium, P_radiated = P_absorbed , and π R_E² is a common factor , so

( 1 - 0.3 ) ( 1.35 kW/m²) = 4(5.67 x 10^-8 W/m²k⁴) T⁴

Therefore,

T⁴ = ( 0.7) (1350 W/m²)/4(5.67 x 10^-8 W/m² K⁴) = 4.17 x 10⁹ K⁴

or T=254 K

Hi aforce20!

(have a pi: π )

The basic equation simply says that the power out must equal the power in.

Which line do you not understand?

 

[aforce20]

I just don't know where to start in solving the problem

 

[aforce20]

Someone please help me through this ?