The sun has a mass of 199e30 kg and is located 15e11 m from...

The sun has a mass of 1.99E30 kg and is located 1.5E11 m from the earth. The average energy per unit time per unit area that reaches the earth's upper atmosphere from the sun is 1.35 kW/m^2. This energy is released by the sun in a series of fusion reactions that fuse four hydrogen nuclei together to form a single helium nucleus. This process releases 4.27E-12 J per helium nucleus created. If we assume the sun to be composed of hydrogen and that it will continue to 'burn' until it has consumed 10% of the available hydrogen, estimate the lifetime of the sun. Answer in units of years. Hint: The surface area of a sphere is 4πr^2. Work with units to see how to proceed.

Transcript

00:01 So the sun has a mass that we're given as 1 .99 times 10 to the 30th kilograms.

00:07 And we're told that each interaction, each fusion interaction, where four hydrogen atoms are combined into helium, produces an energy, we'll call this delta e, or an energy yield of about 4 .27 times 10 to the negative 12 joules.

00:28 And so we're told that the intensity of sun.

00:31 Sunlight at earth's surface is 1 .35 kilowatts per square meter, right? and if the distance to the sun is approximately 150 billion meters, then we kind of want to estimate how much longer the sun has if it's going to burn hydrogen until it's burned up 10 % of its current volume.

00:53 So like the change in mass that we're looking for is going to be basically 1 .99 times 10 to the 29th.

01:01 Kilograms.

01:04 All right.

01:04 So this may seem kind of jumbled and incoherent, but what we want to do is relate this intensity here to the amount of power produced by the sun, the amount of energy produced every second.

01:15 And we can do that.

01:16 We can calculate the power because this will be the intensity times 4 pi d squared.

01:23 D is this distance right here.

01:25 And so this is going to be, let's write it in watts per square meter, because we'll need to make that conversion.

01:32 Later on anyway.

01:34 So, 1 ,350 times 4 pi times 2 .25 times 10 to the 22nd square meters.

01:41 This is what we've got here.

01:43 This gives us the power output of the sun at the surface of the sun.

01:47 This comes out to about 3 .817 times 10 to the 26 watts...