Using your knowledge of the suns luminosity (3.8x10^26 Watts) and temperature (5800k) calculate the suns diameter

Answer 1

Use the Stefan-Boltzmann law.

P = power output in Watts (given)

d = diameter in meters

A = surface area = 4π(d/2)² = πd²

T = absolute temperature in Kelvins (given)

σ = Stefan-Boltzmann constant. Look it up in your book in units of W/(m²K⁴).

P = AσT⁴

P = πd²σT⁴

d = [P/(πσT⁴)]^1/2

Plug in the numbers, evaluate, and get d in meters.