Radiation, temperature of earth, heat transfer

AI Thread Summary
The discussion revolves around calculating the Earth's surface temperature based on its radiation emission of 54E-3 J/s, assuming it behaves as a perfect black body. The initial calculation yields a temperature of 31.2 K, but there is uncertainty regarding the accuracy of the Q/t value and the implications of such a low temperature. Participants question whether the given emission rate is correct, as it suggests an unrealistic surface temperature of -271 C. The consensus leans towards the calculated value being too high for the Earth's actual conditions. Ultimately, the conversation highlights the complexities in thermal radiation calculations and the assumptions made in the scenario.
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If an area of 1 m2 at the Earth surface emits Q/t = 54E-3 J/s in radiation, what would the temperature at the Earth surface be, if there would be no other energy sources? Assume that the Earth is a perfect black body emitter (e = 1).

Q/t = e(5.67E-8)(A)T4
54E-3 = 1(5.67E-8)T4
T = 31.2 K?

The answer is supposed to be 2.4 K? I feel pretty confident in my work so I am not certain where I have gone wrong.
 
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Are you sure your Q/t is correct? The surface of the Earth is really -271 C?
 
Given the numbers given in the problem statement, I agree with the 31.2 K value. It does sound silly to say this takes place somewhere on the Earth's surface though.
 

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