Heat and Thermodynamics 3 Question 20
20. The intensity of radiation emitted by the sun has its maximum value at a wavelength of $510 nm$ and that emitted by the north star has the maximum value at $350 nm$. If these stars behave like black bodies, then the ratio of the surface temperature of the sun and the north star is
(1997, 1M)
(a) 1.46
(b) 0.69
(c) 1.21
(d) 0.83
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Solution:
- From Wien’s displacement law
$$ \begin{array}{rlrl} \text { or } & T & =\frac{1}{\lambda _m} \\ \therefore \quad & \frac{T _{\text {sun }}}{T _{\text {north star }}} & =\frac{\left(\lambda _m\right) _{\text {north star }}}{\left(\lambda _m\right) _{\text {sun }}} \\ & =\frac{350}{510} \approx 0.69 \end{array} $$
$$ \lambda _m T=\text { constant } $$
