Final answer:
The total power radiated by the Sun into space is calculated using the Stefan-Boltzmann law, where the power radiated per unit area is proportional to the fourth power of its temperature. With the Sun's radius, we can find its surface area to determine the total power emitted.
Step-by-step explanation:
The total power radiated into space by the sun, assuming it is a perfect emitter at 6000 K, can be estimated using the Stefan-Boltzmann law. This law states that the power radiated per unit area (P/A) of a black body is proportional to the fourth power of the black body's temperature (T). The equation P/A = σT4 includes the Stefan-Boltzmann constant (σ) and can be rearranged to P = AσT4 to find the total power (P) radiated by a spherical object like the Sun.
To apply this to the Sun, we need to calculate the sun's surface area (A) using the formula A = 4πR2, where R is the radius of the Sun. Given that the radius (R) of the Sun is 7.0×108 m, we can find the surface area. With σ = 5.67×10−8 W/m2K4 and T = 6000 K, the total power (P) can be calculated.
The calculation would be P = 4π(7.0×108 m)2×5.67×10−8 W/m2K4×(6000 K)4, which yields the total power the Sun radiates into space.