Radiation, temperature of earth, heat transfer

[bulbasaur88]

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.

 

[RTW69]

Are you sure your Q/t is correct? The surface of the Earth is really -271 C?

 

[Redbelly98]

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.