Black Body Examples
Question:
What is the temperature of the Sun's surface, given that the
maximum of its intensity is at 500 nm?
Answer:
Wien's law:
Question:
By how much would the Sun's temperature have to increase to triple
the amount of radiation it emits?
Answer:
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\[ \rm \mathbf{ \frac{I'}{I} = \frac{T'^{4}}{T^{4}} \Rightarrow T'^{4} = \frac{I'}{I}
T^{4} \Rightarrow T' = \frac{I'}{I}^{1/4} T} \]
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Since I'/I= 3, and T = 5.8$\cdot$ 103 K, we find:
T' = 31/4 $\cdot$ 5.80$\cdot$ 103
K = 7.63$\cdot$ 103 K
The increase would be (7.63 - 5.80)$\cdot$ 103
K = 1830 K
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MultiMedia Physics
2000