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ma18
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Homework Statement
How much time does it take a planet with surface temperature of 100K and a radius of 500 km to cool down to 50K, ignoring solar heating. Assume E_thermal = 3/2 NkT and that the surface radiates as a blackbody. Calculate this by using the relationship between thermal energy and temperature and the relationship between the rate of energy loss dE/dt and temperature.
Homework Equations
E_thermal = 3/2 NkT
Power emitted/Area = σT^4
The Attempt at a Solution
Power = Energy/Time
Energy/Area*Time = σT^4
Energy = σT^4 * A*t
Subbing for thermal energy
3/2 NkT = σT^4 * A*t
T = (3NKt/2A)^(1/3)
I feel like I've missed something and the T should be a delta T but I'm not sure where I've going wrong.
Thanks for any help,
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