SATHEE: Heat and Thermodynamics 3 Question 28

Heat and Thermodynamics 3 Question 28

28. Two spherical stars $A$ and $B$ emit black body radiation. The radius of $A$ is 400 times that of $B$ and $A$ emits $10^{4}$ times the power emitted from $B$ . The ratio $(\frac{λ_{A}}{λ_{B}})$ of their wavelengths $λ_{A}$ and $λ_{B}$ at which the peaks occur in their respective radiation curves is

(2015 Adv.)

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Solution:

Power, $P = (σ T^{4} A) = σ T^{4} (4 π R^{2})$

or, $P \propto T^{4} R^{2}$

According to Wien’s law,

$λ \propto \frac{1}{T}$

( $λ$ is the wavelength at which peak occurs)

$∴$ Eq. (i) will become,

$\begin{matrix} P \propto \frac{R^{2}}{λ^{4}} or λ \propto {[\frac{R^{2}}{P}]}^{1 / 4} \\ \Rightarrow \frac{λ_{A}}{λ_{B}} = {[\frac{R_{A}}{R_{B}}]}^{1 / 2} {[\frac{P_{B}}{P_{A}}]}^{1 / 4} = [400]^{1 / 2} {[\frac{1}{10^{4}}]}^{1 / 4} = 2 \end{matrix}$

Heat and Thermodynamics 3 Question 28

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Heat and Thermodynamics 3 Question 28

28. Two spherical stars A and B emit black body radiation. The radius of A is 400 times that of B and A emits 104 times the power emitted from B. The ratio (λAλB) of their wavelengths λA and λB at which the peaks occur in their respective radiation curves is

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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