Kinetic Theory of Gases and Radiation — Physics STD 12 Science — Question
Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsKinetic Theory of Gases and Radiation3 Marks
Question
Explain the Stefan-Boltzmann law.
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Answer
The power per unit area radiated from the surface of a blackbody at an absolute temperature $\mathrm{T}$ is its emissive power or radiant power $\mathrm{R}_{\mathrm{b}}$ at that temperature. According to the Stefan- Boltzmann law, $\mathrm{R}_{\mathrm{b}} \propto \mathrm{T}^4 \therefore \mathrm{R}_{\mathrm{b}}=\sigma \mathrm{T}^4$ where the constant a is called Stefan's constant. If $\mathrm{A}$ is the surface area of the body, its radiant power, i.e., energy radiated per unit time, is $\mathrm{A}^4 \mathrm{~T}^4$. [Note : This law was deduced by Josef Stefan (1835-93), Austrian physicist, from the experimental results obtained by John Tyndall (1820-93), British physicist. The theoretical derivation of this law is due to Boltzmann in 1884. Hence, the law is known as the StefanBoltzmann law. $ \begin{aligned} & \sigma=5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^2 \cdot \mathrm{K}^4 \\ & {[\sigma]=\left[\mathrm{L}^0 \mathrm{M}^1 \mathrm{~T}^{-3} \Theta^{-4}\right] \text {, where } \Theta \text { denotes the dimension of }} \\ & \text { temperature. }] \end{aligned} $
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