Heat Transfer, Blackbody Radiation

[tiffancy1]

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.

 

[alphysicist]

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.