(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Derive the radiative timescale for an atmosphere:

[tex]

\tau_{E} = \frac{c_{p} p_{0}}{4 g \sigma T^{3}_{E}}

[/tex]

2. Relevant equations

As above

3. The attempt at a solution

I've gathered that the difference between the radiative power of an object,

[tex]

\sigma (T + \Delta T)^{4}

[/tex]

And the incoming solar flux on the object, [tex](1 - \sigma) S[/tex], is equal to an instantaneous rate of change of heat, [tex]\frac{dQ}{dt}[/tex]. I don't know how to proceed from here; my derivation of the answer doesn't appear to conform to the one above.

edit: oh for crying out loud, I hate TeX. It never does what I want it to, and I have the 'how to program tex' thread open here in front of me. You can see what I was trying to achieve.

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# Meteorology - radiative equilibrium timescale

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