Please answer the question fully for points Until the mid-twentieth century, peo
ID: 2107404 • Letter: P
Question
Please answer the question fully for points
Until the mid-twentieth century, people couldn't understand how the sun could possibly emit so much energy (in the form of heat and light) over such a long period of time. Not knowing about nuclear reactions, they assumed that the sun burned fuel, like wood for example, to generate its energy. Your goal is to calculate the expected lifetime of the sun if it were made entirely of firewood. Here are five relevant facts: The distance of the sun to the Earth is about R = 93 million miles. The surface area of any sphere of radius R is Surface Area = 4piR2. The energy reaching us on the Earth from the Sun is about 1 kilowatt per square meter. (That means that if you put a square meter of cardboard on the ground, it will soak up 1000 joules of energy from the Sun every second.) Firewood has an energy content of about 15 megajoules per kilogram. (Note: 1 megajoule = 106 joules). The mass of the sun, as determined from Newton's Universal Law of Gravity, is msum = 2 * 1030kg. Using the above facts, calculate the expected lifetime of the sun in years, assuming the sun is made of burning firewood.Explanation / Answer
R = 93 million miles = 93 * 10^6 * 1609.34 meters = 149669 * 10^6 m
A = area = 4 pi R^2 = 4 * 3.1416*149669e6 * 149669e6 = 2.81498e23 m2
the power of the sun = P = 1000 * 2.81498e23 = 2.81498 * 10^26 Watts
energy of the sun = E = (2 * 10^30) * (15 * 10^6) = 30 * 10^36 J
t = E/P = (30 * 10^36)/(2.81498 * 10^26) = 1.07 * 10^11 seconds = 1233480 days