Radiation
Consider some nuclear waste is buried underground in a 1 m diameter spherical capsule with a surface emissivity of 0.5. If the measured absolute temperature is 300°C, what is the radiation emitted by the capsule in Watts?
Expand Hint
For radiation emitted by a body:
$$$\dot{Q}=\varepsilon \sigma AT^4$$$
where
$$\varepsilon$$
is the body’s emissivity,
$$\sigma$$
is the Stefan-Boltzmann constant
$$=5.67 \times 10^{-8}W/(m^2 \cdot K^4)$$
,
$$A$$
is the body’s surface area, and
$$T$$
is the absolute temperature.
Hint 2
Surface area of a sphere:
$$$A=4\pi r^2$$$
where
$$r$$
is the sphere’s radius.
Surface area of a sphere:
$$$A=4\pi r^2$$$
where
$$r$$
is the sphere’s radius.
$$$A=4\pi (\frac{1m}{2})^2=3.14\:m^2$$$
For radiation emitted by a body:
$$$\dot{Q}=\varepsilon \sigma AT^4$$$
where
$$\varepsilon$$
is the body’s emissivity,
$$\sigma$$
is the Stefan-Boltzmann constant
$$=5.67 \times 10^{-8}W/(m^2 \cdot K^4)$$
,
$$A$$
is the body’s surface area, and
$$T$$
is the absolute temperature.
$$$\dot{Q}=(0.5)(5.67\cdot 10^{-8}\frac{W}{m^2\cdot K^4})(3.14m^2)(300+273K)^4$$$
$$$=(1.57)(5.67\cdot 10^{-8}\frac{W}{K^4})(573K)^4=9,596\:W$$$
9,596 W
Time Analysis
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