Why does the sun shine?

How long will the sun be able to shine?

• The sun has a mass of about 2.0 × 1030 kg and radiates energy at a rate of roughly 3.6 × 1026 W. Imagine that the sun was a big ball of burning gasoline suspended in an oxygen atmosphere. About how long would the sun be able to shine? (1 g of gasoline releases about 44,000 J of energy when it burns. The discrepancy between the sun’s age estimated this way and other evidence of the earth’s great age was quite disconcerting to physicists until the process of fusion was discovered.) Hint: The mass of the sun is 2.0 x 1030 kg and you will need to know how many seconds are in a year. I'm beyond stuck on this. I don't even know where to begin. Any help will be appreciated!

• Answer:

  1g releases 44,000J of energy. The sun radiates 3.6*10^26 Joules per second. So the sun is using up (3.6 * 10^26)/44000 = 8,181,818,181,818,181,818,182 g/s or about 8.2 x 10^21 g/s. That means the sun would last about 2.4 x 10^11 seconds which is 6.8*10^7 hours or 7.8 thousand years. Thankfully the sun is not a ball of gasolene, which is a relatively inefficient means of storing and releasing energy (from the breaking and forming of chemical bonds) but rather energy is converted to mass according to E=mc^2, so the sun will actually last another 5 billion years.