Solving Atmosphere Layers: Deriving Equations for Venus Surface & Atmos. Temp.

[Sunshin3]

1. Homework Statement
Consider a one layer atmosphere for the planet Venus. 19% of incoming solar radiation is absorbed by the atmosphere. 99% of the outgoing radiation is absorbed by the atmosphere. The incoming radiation, E, as measured by satellite is 615 Wm-2.

1) Derive two equations, one for the top of the atmosphere and the other for the Venusian surface in terms of x, y and E. Solve for the surface and atmospheric temperatures.

Homework Equations

None we need to create the equations but i do not know where to start.

The Attempt at a Solution

Please help! i have no clue where to start

 

[Andrew Mason]

If 19% of the incoming radiation from the sun is absorbed, what happens to the other 81%? If the whole atmosphere is in thermal equilibrium, what must the lower atmosphere radiate back out?

AM

 

[kerimek]

.

I would approach this problem by first understanding the basic principles of energy balance in a one layer atmosphere. The first equation we need to consider is the energy balance at the top of the atmosphere, which can be written as:

E = F + R

Where E represents the incoming solar radiation, F represents the outgoing radiation from the atmosphere, and R represents the reflected solar radiation. We know that 19% of E is absorbed by the atmosphere, so we can rewrite the equation as:

E = 0.19E + F + R

Since we are given that 99% of the outgoing radiation is absorbed by the atmosphere, we can also write the equation as:

E = 0.19E + 0.99F

Now, we can solve for F by rearranging the equation:

F = (E - 0.19E)/0.99

F = 0.808E

Next, we need to consider the energy balance at the surface of Venus. We can write the equation as:

E = F + R + S

Where S represents the heat transfer from the surface to the atmosphere. We know that the surface absorbs all of the outgoing radiation from the atmosphere, so we can write the equation as:

E = F + S

Substituting the value of F from the previous equation, we get:

E = 0.808E + S

Solving for S, we get:

S = (1-0.808)E

S = 0.192E

Now, we can use the Stefan-Boltzmann law to relate the heat transfer from the surface to the temperature of the surface, which can be written as:

S = σT^4

Where σ is the Stefan-Boltzmann constant and T is the temperature of the surface. We can rearrange this equation to solve for T:

T = (S/σ)^(1/4)

Substituting the value of S, we get:

T = (0.192E/σ)^(1/4)

Finally, we can use the same equation to relate the heat transfer from the atmosphere to the atmospheric temperature. Since we know that 99% of the outgoing radiation is absorbed by the atmosphere, we can write the equation as:

F = σT^4

Substituting the value of F, we get:

0.808E = σT^4

Solving for T