Heat Transfer, Blackbody Radiation

In summary, the solar constant is the amount of energy received from the Sun on a 1.000 m2 area oriented perpendicular to the direction of sunlight, with a value of about 1.37 kW/m2. The equilibrium temperature of an asphalt pavement illuminated by sunlight and surrounded by a 30°C environment can be calculated using Stefan's Law, taking into account the radiation from the surroundings and the power gained from the solar constant. The area does not need to be included in the calculation.
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Homework Statement



The solar constant is the amount of energy from the Sun we receive on the Earth during each second on a 1.000 m2 area oriented perpendicular to the direction of the sunlight. The value of the solar constant is about 1.37 kW/m2. Imagine sunlight illuminating an asphalt pavement as indicated in Figure P.63. The ambient temperature is 30°C. What is the equilibrium temperature of the asphalt? Assume the asphalt is a blackbody.

Answer is in Celsius*

Homework Equations



Stefan's Law: dQ/dt = -e(A)([tex]\sigma[/tex])(T^4)
where [tex]\sigma[/tex] = 5.670 x 10^-8 W/(m^2 x K^4)

Blackbody radiation so the e value should be 1.

The Attempt at a Solution



I don't understand how to incorporate the solar constant into the equation. Is the area just 1m^2? I'm lost! =( PLEASE HELP! THANK YOU.
 
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  • #2
Hi tiffancy1,

There are three processes going on here: the asphalt is gaining energy from the sunlight, the asphalt is gaining energy from radiation from its surroundings at 30 degrees C, and the asphalt is losing energy by radiation.

You can write an expression relating the power from these three. Stefan's law describes the radiation, and the solar constant can give you the power gained by the sunlight. (Make sure you notice the units.)

You do not need the area; it should cancel.
 
  • #3




To incorporate the solar constant into the equation, we can use the definition of power (P = dQ/dt) and the given value of the solar constant (1.37 kW/m2) to find the rate of energy being transferred to the asphalt. This would give us the value for dQ/dt, which we can then plug into the Stefan's Law equation along with the other given values (e = 1, A = 1m2, and \sigma = 5.670 x 10^-8 W/(m^2 x K^4)). This will allow us to solve for the equilibrium temperature (T) of the asphalt. Remember to convert the solar constant from kW/m2 to W/m2 before plugging it into the equation. I hope this helps.
 

1. What is heat transfer?

Heat transfer is the process of moving thermal energy from one object or system to another. This can occur through three main mechanisms: conduction, convection, and radiation.

2. What is blackbody radiation?

Blackbody radiation refers to the electromagnetic radiation emitted by a perfect absorber and emitter of radiation, known as a blackbody. This type of radiation is emitted by all objects with a temperature above absolute zero and is characterized by a continuous spectrum of wavelengths.

3. How does heat transfer through conduction?

Conduction is the transfer of heat through direct contact between two objects or substances. This occurs when the particles in one object vibrate and transfer their energy to the particles in the other object, causing them to vibrate and increase in temperature.

4. What is convection heat transfer?

Convection heat transfer involves the transfer of heat through the movement of fluids, such as air or water. This occurs as the hotter particles in the fluid rise and are replaced by cooler particles, creating a continuous cycle of heat transfer.

5. How does radiation heat transfer work?

Radiation heat transfer is the transfer of heat through electromagnetic waves. All objects with a temperature above absolute zero emit radiation, and this radiation can be absorbed by other objects, causing an increase in temperature.

Suggested for: Heat Transfer, Blackbody Radiation

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