Did you mean ##r^2=…##?PMNIMG said:Homework Statement: Use the Stefan-Boltzmann's Law and calculate Sun's radius.
T☉=5772K
L☉= 3.828×10^(26) W
Relevant Equations: E=σT^4
L=4πr^2*σT^4
r=(L/4π*σT^4)^(1/2)
r=(3.828*10^(26))/(4π*σ(5772)^4)
It's diffrent from what I know...
Oh, sorry. I modified it now.haruspex said:Did you mean ##r^2=…##?
Other than that, what is stopping you?
No problem.PMNIMG said:Oh, I think I miscalculated...
sorry I disturbed you all with dumb question...
I think I put km instead of m...
Stefan-Boltzmann's Law states that the total energy radiated per unit surface area of a black body is directly proportional to the fourth power of its absolute temperature. Mathematically, it is expressed as \( E = \sigma T^4 \), where \( E \) is the emissive power, \( \sigma \) is the Stefan-Boltzmann constant, and \( T \) is the absolute temperature in Kelvin.
Stefan-Boltzmann's Law can be applied to the Sun by treating it as an approximate black body. By knowing the Sun's surface temperature (around 5778 K) and using the Stefan-Boltzmann constant, we can calculate the total energy output per unit area of the Sun's surface. This helps in determining the Sun's luminosity, which is the total energy radiated by the Sun per second.
The Stefan-Boltzmann constant (\( \sigma \)) is a physical constant denoted by \( \sigma \) and has a value of approximately \( 5.67 \times 10^{-8} \) W/m²K⁴. It is used in the Stefan-Boltzmann Law to relate the temperature of a black body to the total energy it radiates.
To calculate the Sun's luminosity, you first determine the energy radiated per unit area using \( E = \sigma T^4 \), where \( T \) is the Sun's surface temperature. Then, multiply this energy by the Sun's surface area \( 4\pi R^2 \), where \( R \) is the Sun's radius. The resulting product gives the Sun's luminosity \( L = 4\pi R^2 \sigma T^4 \).
The Sun is considered an approximate black body because it emits a spectrum of radiation that closely follows the black body radiation curve. Although the Sun is not a perfect black body, it emits radiation across a wide range of wavelengths, and its emission can be reasonably approximated using black body radiation principles, allowing us to apply Stefan-Boltzmann's Law to estimate its energy output.