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(A) According to the Stefan-Boltzmann law,the total energy $E$ radiated per unit area per unit time by a black body is proportional to the fourth powe

Vedclass · Accepted Answer

$E \propto T^{4}; E_{max} \propto T^{5}$

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(A) According to the Stefan-Boltzmann law,the total energy $E$ radiated per unit area per unit time by a black body is proportional to the fourth power of its absolute temperature: $E \propto T^{4}$.According to Wien's displacement law,the wavelength $\lambda_{max}$ corresponding to maximum energy emission is inversely proportional to temperature: $\lambda_{max} \propto 1/T$.The spectral energy density $E_{\lambda}$ is given by Planck's law. The maximum spectral energy density $E_{max}$ at a given temperature $T$ is proportional to the fifth power of the absolute temperature: $E_{max} \propto T^{5}$.Therefore,the correct relationship is $E \propto T^{4}$ and $E_{max} \propto T^{5}$.

If $E$ is the total energy emitted by a body at temperature $T \ K$ and $E_{max}$ is the maximum energy emitted by it at the same temperature,then:

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