the energy received by the earth from the sun is 1400w/m2. Assuming that the sun is a black body radiator and the ratio of the radius of the earth's orbit to the sun's radius is 216. Calculate the surface temperature of the sun. Stefan constant = 0.000000057w/m2 k4.
To calculate the surface temperature of the sun, we can use the Stefan-Boltzmann law, which relates the energy radiated by a black body to its temperature. The law states that the power radiated per unit area (P) is proportional to the fourth power of the temperature (T) and is given by the equation:
P = σ * T^4
Where:
P is the power radiated per unit area (in watts per square meter, W/m^2)
σ is the Stefan-Boltzmann constant (0.000000057 W/m^2 K^4)
T is the temperature of the black body (in Kelvin, K)
In this case, we know that the energy received by the Earth from the sun is 1400 W/m^2. Since the Earth is at a distance from the sun, we need to take into account the inverse square law, which states that the intensity of radiation decreases as the square of the distance (d) between the two objects:
I = E / (4πd^2)
Where:
I is the intensity of radiation received by Earth (in W/m^2)
E is the energy received by Earth from the sun (in W/m^2)
d is the distance between the Earth and the sun (in meters)
We also know that the ratio of the Earth's orbit radius (r_earth) to the sun's radius (r_sun) is 216:
r_earth / r_sun = 216
Using this information, we can calculate the distance between the Earth and the sun:
d = (r_earth + r_sun) = (216 +1) * r_sun = 217 * r_sun
Now, we can substitute the values into the equation for intensity to find E:
I = E / (4πd^2)
1400 W/m^2 = E / (4π(217 * r_sun)^2)
We can solve this equation for E to find the energy received by the Earth.
Once we find E, we can substitute it into the Stefan-Boltzmann law to find the temperature (T) of the sun's surface:
E = σ * T^4
Solving this equation for T will give us the surface temperature of the sun.