Heat Transfer, Blackbody Radiation

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SUMMARY

The discussion centers on calculating the equilibrium temperature of asphalt, treated as a blackbody, when illuminated by sunlight with a solar constant of 1.37 kW/m². The key equation utilized is Stefan's Law: dQ/dt = -e(A)(σ)(T^4), where σ is 5.670 x 10^-8 W/(m² x K^4) and the emissivity (e) is 1 for a blackbody. Participants clarify that the area does not need to be specified as it cancels out in the calculations, and the asphalt gains energy from both sunlight and ambient radiation while losing energy through radiation.

PREREQUISITES
  • Understanding of Stefan's Law and its application in heat transfer.
  • Knowledge of blackbody radiation principles.
  • Familiarity with solar constants and their significance in energy calculations.
  • Basic algebra and unit conversion skills for energy calculations.
NEXT STEPS
  • Study the derivation and applications of Stefan's Law in thermal physics.
  • Explore the concept of blackbody radiation and its implications in real-world scenarios.
  • Research the solar constant and its variations based on atmospheric conditions.
  • Learn about energy balance equations in thermodynamics and their applications in environmental science.
USEFUL FOR

Students in physics or engineering, educators teaching thermodynamics, and professionals involved in environmental science or energy management will benefit from this discussion.

tiffancy1
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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)(\sigma)(T^4)
where \sigma = 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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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.
 

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