The sun radiates energy at the rate of 6.5 x 10 to the power of 7 w/m squared.Assuming that the sun radiates as a black body(which approximate true), find its surface temperature.
6200K
To find the surface temperature of the sun, we can use the Stefan-Boltzmann law, which states that the power radiated by a black body per unit area is proportional to the fourth power of its temperature. The formula is given by:
P = σ * A * T^4
Where:
P = Power radiated (6.5 x 10^7 W/m^2)
σ = Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4)
A = Surface area of the sun (unknown)
T = Temperature of the sun (unknown)
To calculate the surface temperature T, we need to rearrange the equation and solve for T:
T^4 = P / (σ * A)
Taking the fourth root of both sides gives:
T = (P / (σ * A))^(1/4)
Now we need to find the surface area A. The surface area of a sphere is given by the formula:
A = 4πR²
Where R is the radius of the sun. The radius of the sun is approximately 6.96 x 10^8 meters.
Calculating A:
A = 4 * π * (6.96 x 10^8)^2
Now we can substitute the values into the temperature formula and calculate the surface temperature:
T = (6.5 x 10^7) / (5.67 x 10^-8 * 4π * (6.96 x 10^8)^2)^(1/4)
By plugging in the values, you can calculate the surface temperature of the sun.
To find the surface temperature of the sun, we can use the Stefan-Boltzmann law. The Stefan-Boltzmann law relates the surface temperature of a black body to the amount of energy radiated per unit area.
The Stefan-Boltzmann law states that the power radiated by a black body is proportional to the fourth power of its temperature (in Kelvin) and the surface area. Mathematically, it can be expressed as:
P = σ * A * T^4
Where:
P is the power radiated per unit area,
σ (sigma) is the Stefan-Boltzmann constant (equal to 5.67 x 10^(-8) W/m^2K^4),
A is the surface area of the black body, and
T is the temperature of the black body in Kelvin.
In this case, we are given the power radiated per unit area (6.5 x 10^7 W/m^2), so we can substitute the values into the equation and solve for T.
6.5 x 10^7 = (5.67 x 10^(-8)) * A * T^4
To find A, we need to know the radius of the sun, which is approximately 6.96 x 10^8 meters. The surface area of the sun can be calculated using the formula for the surface area of a sphere:
A = 4πr^2
A = 4 * 3.1416 * (6.96 x 10^8)^2
Substituting this value of A into the equation, we have:
6.5 x 10^7 = (5.67 x 10^(-8)) * (4 * 3.1416 * (6.96 x 10^8)^2) * T^4
Now we can solve for T:
T^4 = (6.5 x 10^7) / [(5.67 x 10^(-8)) * (4 * 3.1416 * (6.96 x 10^8)^2)]
T^4 = 1.57 x 10^15
Taking the fourth root of both sides:
T = (1.57 x 10^15)^(1/4)
T = 5776 K
Therefore, the surface temperature of the sun is approximately 5776 Kelvin.