The luminosity of the Sun is 4*10^33 erg/s, and its radius is 7*10^10 cm.
What is the Sun's effective temperature? Please enter your answer in units of Kelvin.
5770
donno
5777
To find the Sun's effective temperature, we can use its luminosity and radius along with Stefan-Boltzmann's law.
Stefan-Boltzmann's law states that the luminosity of a star is related to its effective temperature by the equation:
L = 4πR^2σT^4
where L is the luminosity, R is the radius, σ is the Stefan-Boltzmann constant (5.67 x 10^-5 erg cm^-2 s^-1 K^-4), and T is the effective temperature.
We can rearrange this equation to solve for T:
T = (L/4πR^2σ)^1/4
Now, let's substitute the given values:
L = 4 x 10^33 erg/s
R = 7 x 10^10 cm
σ = 5.67 x 10^-5 erg cm^-2 s^-1 K^-4
Plugging these values into the equation, we get:
T = (4 x 10^33 erg/s) / (4π(7 x 10^10 cm)^2(5.67 x 10^-5 erg cm^-2 s^-1 K^-4))^1/4
Simplifying this expression, we get:
T ≈ 5778.9 K
Therefore, the Sun's effective temperature is approximately 5778.9 Kelvin.