define spectral emittance and say how one obtains the total intensity
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Distinguish between emissive power and spectral emissive power.
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The electromagnetic intensity of all wavelengths thermally radiated by a body of temperature $T$ is given by $$I=\sigma T^{4} \text { where } \sigma=5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}^{4}$$ This is the Stefan-Boltzmann Jaw. To derive it. show that the total energy of the radiation in a volume $V$ at temperature $T$ is $U=8 \pi^{5} k_{\mathrm{B}}^{2} / 7^{4} / 15 h^{3} c^{3},$ by integrating Planck's spectral energy density over all frequencies. Note that $\int_{0}^{\infty} \frac{x^{3}}{e^{x}-1} d x=\frac{\pi^{4}}{15}$ Intensity, or power per unit area, is then the product of energy per unit volume and distance per unit time. But because intensity is a flow in a given direction away from the blackbody, $c$ is not the correct speed. For radiation moving uniformly in all directions, the average component of velocity in a given direction is $\$$ c.
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