# Find the total amount of energy generated by each gram of solar matter over the entire lifetime of the sun

My textbook gives me this information: Quantify how efficiently the sun generates energy by dividing the solar luminosity by the solar mass, which is this:

4 x 10^26W / 2 x 10^30kg = 2 x 10^-4W/kg

so every kilogram of solar material yields about 0.2 milliwatt of energy or 0.0002 joule (J) of energy every second.

Then my textbook says "we must consider the total amount of energy generated by each gram of solar matter over the entire lifetime of the Sun as a star" and the instructions to do that say "simply multiply the rate at which the Sun generates energy by the age of the sun (about 5 billion years)"

The book doesn't show the steps of the answer, it just states: "We obtain a value of 3 x 10^13 J/kg"

No matter how hard I tried, I could not find that same answer with the numbers I had been given. I tried working backwards, by dividing the given value and the age of the sun:

3 x 10^13/5 x 10^9 = x

But with that I got 3/5 x 10^4, a number that isn't provided.

What am I doing wrong?

• I like physics, but this is a math forum. Maybe this could go into dimensional analysis Commented Mar 17, 2015 at 20:01

$$\frac{5\times10^9 \textrm{ years}}{1}\frac{3.15\times10^7\textrm{ sec}}{\textrm{year}}\frac{0.0002\textrm{ J}}{\textrm{kg sec}} = 3.15\times10^{13} \frac{J}{kg}$$