Please help assign due 2marrow effective radiative temperature

[Sunshin3]

. Homework Statement

It is believed that in the Archeaneon (2.5-4 billion years ago) the sun’s radiative output was 30% less than it is today.

(i) What would the temperature of the sun have been at that time?

(ii) At what wavelength would the peak emission from the sun have been?

(iii) Ignoring the effects of the atmosphere, what would the temperature of the Earth have been at this time (i.e. the effective radiative temperature)? Assume that the Earth’s albedo was 0.3, the same as today.


2. Homework Equations
Boltzman equation
wiens law

3. The Attempt at a Solution

a)T= 4th root[5143824/(5.67*10^-8)]
t=5488.14K

b)detlamax=2897/5488.147
=0.527

I DONT GET PART 3 PLEASE HELP MEE! MY ASSIGNMENT IS DUE TOMARROW! PLEASE

 

[Andrew Mason]

You will have to do a better job of explaining your work in parts 1 and 2.

To do part 3, you have to determine what amount of radiation the Earth currently receives / unit time and then reduce it by 30%. You know that the Earth must radiate that same amount of energy /unit time (on average). From that, apply the Stefan-Boltzmann law to determine its temperature.

AM

 

[kerimek]

HELP

For part (iii), we can use the Stefan-Boltzmann law to calculate the effective radiative temperature of the Earth. The Stefan-Boltzmann law states that the energy radiated from a blackbody is proportional to the fourth power of its temperature. In this case, we can assume that the Earth is a blackbody and use the following equation:

T = (L/4πσR^2)^1/4

Where:
T = temperature in Kelvin
L = luminosity of the sun
σ = Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4)
R = distance between the Earth and the sun (assume 1 AU)

Using the luminosity of the sun at that time (30% less than today), we can calculate the effective radiative temperature of the Earth. Remember to convert the luminosity to SI units (Watts) before plugging it into the equation.

Once you have calculated the effective radiative temperature of the Earth, you can then use the albedo value (0.3) to calculate the equilibrium temperature of the Earth using the following equation:

Te = (1-A)^1/4 * T

Where:
Te = equilibrium temperature of the Earth
A = albedo value (0.3)
T = effective radiative temperature of the Earth calculated in the previous step

This will give you the temperature of the Earth at that time, assuming there were no atmospheric effects. Keep in mind that this is a simplified calculation and does not take into account other factors such as the greenhouse effect.