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:

  1. 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, $\quad T _1>T _3>T _2$



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