Question

At our distance from the Sun, the intensity of solar radiation is 1 370 W/m2. The temperature of the Earth is affected by the greenhouse effect of the atmosphere. This phenomenon describes the effect of absorption of infrared light emitted by the surface so as to make the surface temperature of the Earth higher than if it were airless. For comparison, consider a spherical object of radius r with no atmosphere at the same distance from the Sun as the Earth.

Assume its emissivity is the same for all kinds of electromagnetic waves and its temperature is uniform over its surface.
Compute its steady-state temperature. Is it chilly?

Answer 1

`5.63498482\ ^(\circ)C`

Step-by-step explanation:

`\sigma` = Stefan-Boltzmann constant =
`5.67* 10^(-8)\ W/m^2K^4`

I = Intensity =
`1370\ W/m^2`

r = Radius

T = Temperature

The power going in is equal to the power going out

`I\epsilon\pi r^2=4\pi r^2\epsilon\sigma T^4\\\Rightarrow T=((I)/(4\sigma))^{(1)/(4)}\\\Rightarrow T=((1370)/(4* 5.67* 10^(-8)))^{(1)/(4)}\\\Rightarrow T=278.78498482\ K`

Converting to Celcius

`278.78498482-273.15=5.63498482\ ^(\circ)C`

So, yes it is chilly