at high noon, the sun delivers 1000w to each square meter of a blacktop road.if the hot asphalt transfers energy only by radiation, what is it's steady-state temperature?
topic??? chemistry, biology physics??
need more information, how much heat is the asphalt radiating?
To find the steady-state temperature of the hot asphalt road, we need to understand how energy is transferred and then apply the appropriate formula.
In this scenario, the sun delivers 1000 watts (W) of energy to each square meter of the blacktop road. The road then transfers this energy only by radiation.
When an object absorbs energy, it heats up until it reaches a steady-state temperature where the incoming energy equals the outgoing energy. In other words, the absorbed energy is radiated back out at the same rate.
To calculate the steady-state temperature using the Stefan-Boltzmann law, we can start by understanding that the power radiated by an object is given by the formula:
P = ε * σ * A * (T^4)
Where:
- P is the power radiated in watts,
- ε is the emissivity of the object (a value between 0 and 1, indicating how well the object radiates energy),
- σ is the Stefan-Boltzmann constant (approximately 5.67 x 10^-8 W/m^2K^4),
- A is the surface area in square meters, and
- T is the temperature of the object in Kelvin.
In this case, we know that the power radiated by the road should equal the power received from the sun, so we can set up an equation:
P = 1000 W
ε * σ * A * (T^4) = 1000
Since we are trying to find the steady-state temperature, we set up the equation and solve for T:
T^4 = (1000) / (ε * σ * A)
T = (1000 / (ε * σ * A))^0.25
Now, we need to know the emissivity (ε) of the blacktop road. The emissivity represents how well an object radiates energy compared to a black body (a perfect emitter of radiation). Since the road is described as "blacktop," we can assume its emissivity is close to 1. For practical purposes, we will use ε = 1.
Using the known value for the Stefan-Boltzmann constant (σ) and the surface area of the road, we can substitute these values into the equation to find the steady-state temperature.
Final Equation:
T = (1000 / (1 * 5.67 × 10^-8 W/m^2K^4 * A))^0.25
Now you can calculate the steady-state temperature by plugging in the appropriate values for the surface area (A) of the road.