A giant star radiates energy at the rate of 3.0 × 10³⁰ W,and its surface temperature has been measured to be 3000 K.Assuming that it is a perfect emitter,what is the radius of this star? (σ = 5.67 × 10^-8 W/m² ∙ K⁴)

Question

Quizplus · Accepted Answer

We can use the Stefan-Boltzmann law to relate the power radiated by the star to its surface area and temperature:

P = σA T^4

where P is the power radiated, A is the surface area, T is the temperature, and σ is the Stefan-Boltzmann constant.

Solving for the surface area:

A = P/(σT^4)

Plugging in the given values:

A = (3.0 × 10^31 W)/(5.67 × 10^-8 W/m^2 K^4 * (3000 K)^4) = 2.32 x 10^19 m^2

Finally, we can use the formula for the surface area of a sphere to find its radius:

A = 4πr^2

r = sqrt(A/(4π)) = sqrt((2.32 x 10^19 m^2)/(4π)) ≈ 2.3 × 10^11 m

Therefore, the correct answer is (E) 2.3 × 10^11 m.

A Giant Star Radiates Energy at the Rate of 3