Question

One of the stars in the orion constellation is sigma orionis with a surface temperature of 28,273 k. It has a radius of 3.4173 million kilometers. Consider the spherical surface to behave as a blackbody radiator. What is the rate (w) at which energy is radiated from this star, to proper sig fig?

a) 3.82 × 10^26 W
b) 5.24 × 10^26 W
c) 6.15 × 10^26 W
d) 7.09 × 10^26 W

Answer 1

The rate at which energy is radiated from the sigma orionis star in the Orion constellation is 3.82 x 10^26 W.

Step-by-step explanation:

To calculate the rate at which energy is radiated from the star, we can use the Stefan-Boltzmann Law, which states that the power radiated by a blackbody is directly proportional to the surface area of the object and its temperature to the fourth power. The formula is given by P = σA(T^4), where P is the power, σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m^2K^4), A is the surface area, and T is the temperature.

First, we need to calculate the surface area of the star. The formula for the surface area of a sphere is A = 4πr^2, where r is the radius. Plugging in the given radius of 3.4173 million kilometers (3.4173 x 10^9 meters), we can calculate the surface area.

A = 4π(3.4173 x 10^9)^2 = 4π(1.1664 x 10^19) = 4.6063 x 10^19 m^2.

Next, we can substitute the values into the formula for power:

P = (5.67 x 10^-8)(4.6063 x 10^19)(28273^4) = 3.82 x 10^26 W.

Therefore, the rate at which energy is radiated from the star is 3.82 x 10^26 W (option a).