Venus's Temperature

Let's ask the question, how hot is Venus?
We don't need to be very exact; we just need a rough estimate.

We deliberately ignore the atmosphere of Venus.

The basic idea:

How much is the energy in?

• Amount of energy received from Sun per square meter per second:
  654 watts/meter²
• Of this, 65% is reflected back into space. So 35% of 654 w/(m² s) is absorbed:
  E_in = 229 watts/meter²

The energy received from the Sun is more than the earth, but a greater fraction is reflected (from the clouds). How much is the energy out?

• To be precise, we want the energy radiated per second per square meter from an "ideal" hot surface called a black body .
• It depends on the temperature T (measured in Kelvins).
• It involves a constant
  (sigma) = 5.7x10^-8 watts/(m² K⁴).

Just set these equal:

(sigma) T⁴ = 229 watts/meter²

so

T⁴ = 229 watts/meter²/(sigma)

or T⁴ = [229 /(5.7x10^-8)] K⁴ = 4.0 x 10⁹ K⁴

We just need the value of T such that T⁴ is 4.0 x 10⁹:

T = 250 K

That's not close at all.
The real surface temperature is 730 K.

But this is more or less right for the temperature at the top of the clouds.

Why is Venus hotter than the blackbody law would suggest?

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