Tag: black body radiation

Questions Related to black body radiation

$\dfrac {watt} {kelvin}$ is the unit of 

stefan's law black body radiation heat transfer thermal properties physics

  1. Stefan's constant

  2. Wien's constant

  3. Cooling's constant

  4. Thermal constant

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Correct Option: A

Assuming the Sun to be a spherical body of radius $R$ at a temperature of $T\ K$. Evaluate the intensity of radiant power, incident on Earth, at a distance $r$ from the Sun where $r _{0}$ is the radius of the Earth and $\sigma$ is Stefan's constant :

stefan's law black body radiation heat transfer thermal properties physics

  1. $\dfrac{R^{2}\sigma T^{4} }{r^{2}}$

  2. $\dfrac{4\pi ^{2}R^{2}\sigma T^{4}}{r^{2}}$

  3. $\dfrac{\pi ^{2}R^{2}\sigma T^{4}}{r^{2}}$

  4. $\dfrac{\pi ^{2}R^{2}\sigma T^{4}}{4\pi r^{2}}$

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Correct Option: A
Explanation:
Total power radiated by the sun

 $=\sigma { T }^{ 4 }\times 4\pi { R }^{ 2 }$

The intensity of power at earth surface

$=\cfrac{\sigma { T }^{ 4 }\times 4\pi { R }^{ 2 }}{4\pi { r }^{ 2 }} \\=\cfrac{\sigma { T }^{ 4 } { R }^{ 2 }}{{ r }^{ 2 }}$

The rectangular surface of area $8 cm \times 4 cm$ of a black body at a temperature of $127^0C$ emits energy at the rate of $E$ per second. If both length and breadth of the surface are reduced to half of its initial value, and the temperature is raised to $327^0C$, then the rate of emission of energy will become :

stefan's law black body radiation heat transfer thermal properties physics

  1. $\dfrac{3}{8}E$

  2. $\dfrac{81}{16}E$

  3. $\dfrac{9}{16}E$

  4. $\dfrac{81}{64}E$

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Correct Option: D
Explanation:
Let $A _1=32$ as given.
Let $A _2$ be the area when length and breadth are reduced by half. Thus the area will be $\dfrac {1}{4}$th of $A _1$
$ \therefore A _2=\dfrac {1}{4} *32=8$
Given $T _1={127}^0C={400}^0K$
Given $T _2={327}^0C={600}^0K$
From Stefan's law $E=\sigma AT^4$
$ \therefore\dfrac{E _1}{E _2}= \dfrac {A _1{T _1}^4}{A _2{T _2}^4}=\dfrac {32*(400)^4}{8*(600)^4}=\dfrac{64}{81}$
$ \therefore \dfrac{E _2}{E _1}= \dfrac{81}{64}$