Heat and Thermodynamics 3 Question 17
17. The plots of intensity versus wavelength for three black bodies at temperatures $T _1, T _2$ and $T _3$ respectively are as shown. Their temperatures are such that
$(2000,2 M)$
(a) $T _1>T _2>T _3$
(b) $T _1>T _3>T _2$
(c) $T _2>T _3>T _1$
(d) $T _3>T _2>T _1$
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Solution:
- Wien’s displacement law for a perfectly black body is
$$ \lambda _m T=\text { constant }=\text { Wien’s constant } b $$
Here, $\lambda _m$ is the minimum wavelength corresponding to maximum intensity $I$.
or
$$ \lambda _m \propto \frac{1}{T} $$
From the figure $\left(\lambda _m\right) _1<\left(\lambda _m\right) _3<\left(\lambda _m\right) _2$
Therefore, $\quad T _1>T _3>T _2$
