Final answer:
The surface temperature of the star can be calculated using the Stefan-Boltzmann law, which relates its luminosity, radius, and temperature. Using the given values of luminosity and diameter, we can calculate the radius of the star and substitute it into the equation to solve for the surface temperature. The surface temperature of the star is approximately 9600 K.
Step-by-step explanation:
The surface temperature of a star can be determined using the Stefan-Boltzmann law, which relates the luminosity (power output) of the star to its surface temperature and radius. The equation is given by:
L = 4πR²σT⁴
Where L is the luminosity, R is the radius, σ is the Stefan-Boltzmann constant, and T is the surface temperature.
In this case, the luminosity of the star is 7.9x10²⁶ W and the diameter (which is twice the radius) is 8.1x10⁸ m. Using these values, we can calculate the radius of the star by dividing the diameter by 2:
R = (8.1x10⁸ m) / 2 = 4.05x10⁸ m
Substituting these values into the equation, we can solve for the surface temperature:
7.9x10²⁶ W = 4π(4.05x10⁸ m)²σT⁴
Simplifying the equation and solving for T:
T⁴ = (7.9x10²⁶ W) / (4π(4.05x10⁸ m)²σ)
T⁴ ≈ 6.1728x10²⁰
Taking the fourth root of both sides:
T ≈ 9600 K
Therefore, the surface temperature of the star is approximately 9600 K.