± Understanding Heat Radiation Learning Goal: To understand the formula for powe

Question

± Understanding Heat Radiation

Learning Goal:

To understand the formula for power radiated in the form of electromagnetic energy by an object at nonzero temperature.

Every object at absolute (Kelvin) temperature T will radiate electromagnetic waves. This radiation is typically in the infrared for objects at room temperature, with some visible light emitted for objects heated above 1000 K. The formula governing the rate of energy radiation from a surface is given by

P=eAT4,

where P is the thermal power (also known as the heat current H).

Part A

This formula applies to _______________.

ANSWER:

This formula applies to _______________.

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?

ANSWER:

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?

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 m on each side and painted black (therefore justifying an emissivity e near unity) emits 2.5 kWat a temperature of 20C. 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?

ANSWER:

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  on each side and painted black (therefore justifying an emissivity  near unity) emits 2.5  at a temperature of 20. 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?

Part D

As a rough approximation, the human body may be considered to be a cylinder of length L=2.0m and circumference C=0.8m. (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=0.6, and the surface temperature is taken to be T=30C, how much thermal power P does the human body radiate?

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

You did not open hints for this part.

ANSWER:

any object of total surface area A, Kelvin temperature T, and emissivity e any object of cross-sectional area A, Kelvin temperature T, and emissivity e any object of total surface area A, Kelvin temperature T, and emissivity any object of cross-sectional area A, Kelvin temperature T, and emissivity

Explanation / Answer

According to the given problem,

A.) Ans: A any object of total surface area A, Kelvin temperature T, and emissivity

B.) Ans: B emissivity

C.) Ans: B The surrounding room is near the temperature of the box and radiates about 2.5 kW of thermal energy into the box.

D.) Ans:

A = LC = 2.0 *0.8 = 1.6 m2

T = 30 + 273 = 303 K

= 0.6

= 5.6704*10-8 (Stefan's constant)

P= eAT4

P = 0.6 * 5.6704 * 10-8*1.6* 3034

P= 458.8338 ~ 460W

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