Part A

This formula applies to $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.$

any object of total surface area AA$,$ Kelvin temperature TT$,$ and emissivity ee

any object of cross$-$sectional area AA$,$ Kelvin temperature TT$,$ and emissivity ee

any object of total surface area AA$,$ Kelvin temperature TT$,$ and emissivity

any object of cross$-$sectional area AA$,$ Kelvin temperature TT$,$ and emissivity

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Part B

If you wanted to find the area of the hot filament in a light bulb, you would have to know the temperature $($determinable from the color of the light$),$ the power input, the Stefan$-$Boltzmann constant, and what property of the filament?

thermal radiation

emissivity

length

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Part C

If you calculate the thermal power radiated by typical objects at room temperature, you will find surprisingly large values, several kilowatts typically. For example, a square box that is $1$ mm on each side and painted black $($therefore justifying an emissivity ee near unity$)$ emits $2\mathrm{.}5$ kWkW at a temperature of $20$C$$C$.$ In reality the net thermal power emitted by such a box must be much smaller than this, or else the box would cool off quite quickly. Which of the following alternatives seems to explain this conundrum best?

The box is black only in the visible spectrum; in the infrared $($where it radiates$)$ it is quite shiny and radiates little power.

The surrounding room is near the temperature of the box and radiates about $2\mathrm{.}5$ kWkW of thermal energy into the box.

Both of the first two factors contribute significantly.

Neither of the first two factors is the explanation.

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Part D

As a rough approximation, the human body may be considered to be a cylinder of length L$=2\mathrm{.}0$mL$=2\mathrm{.}0$m and circumference C$=0\mathrm{.}8$mC$=0\mathrm{.}8$m$.($To simplify things, ignore the circular top and bottom of the cylinder, and just consider the cylindrical sides.$)$ If the emissivity of skin is taken to be e$=0\mathrm{.}6$e$=0\mathrm{.}6,$ and the surface temperature is taken to be T$=30$CT$=30$C$,$ how much thermal power PP does the human body radiate?

Express the power radiated numerically; give your answer to the nearest $10$ WW$.$