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Emissivity e ...

Question

Emissivity $e$ is a property of surface. Suppose for a surface emissivity $e$ varies with Kelvin temperature $T$ as $e = C T$ ( $C$ is constant). If energy emission rate at temperature $600 K$ from the surface is $160 W$ , what will be the energy emission rate (in $watt)$ at $300 K$ ?

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Solution

Given,

Emissivity, $e = C T$

$Δ E = 160 W$

$T_{1} = 600 K$

$T_{2} = 300 K$

According to Stefan’s law.

Energy radiated, $Δ E_{T} = σ e T^{4}$

$Δ E_{T} = σ C T^{5} (∵ e = C T)$

$\frac{Δ E_{T_{1}}}{Δ E_{T_{2}}} = \frac{T_{1}^{5}}{T_{2}^{5}}$

$\frac{160}{Δ E_{T_{2}}} = 2^{5}$

$Δ E_{T_{2}} = 5 W$

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