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Net radiation between a small surface at T_s and a much larger surrounding at T_sur is approximately:
A{'text': "$q'' = \\sigma(T_s + T_{sur})$", 'label': 'A'}
B{'text': "$q'' = \\varepsilon\\sigma(T_s^4 - T_{sur}^4)$", 'label': 'B'}
C{'text': "$q'' = h(T_s - T_{sur})$", 'label': 'C'}
D{'text': "$q'' = k(T_s^2 - T_{sur}^2)$", 'label': 'D'}
Answer & Solution
Correct answer: B. {'text': "$q'' = \\varepsilon\\sigma(T_s^4 - T_{sur}^4)$", 'label': 'B'}
Surface-to-surrounding net radiation: $\varepsilon\sigma(T_s^4 - T_{sur}^4)$. Note BOTH temperatures appear to the FOURTH power; both must be in absolute (Kelvin) units.
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