How long would the Sun burn if it was a huge fire releasing chemical energy?
Assume that the Sun begins with 10^8 joules per kilogram.
The Sun is 1.99*10^30 kg.
I have no idea what formula to use.
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the luminosity of the sun is a wattage, which is Joules per second. so divide the energy density of the sun as given (10^8 joules per kilogram) by the luminosity (joules per second), and you get a value in seconds per kilogram. this is the amount of time the sun will last per kilogram, obviously. multiply this number by the mass of the sun (in kg, as given) and you end up with a time in seconds. this is the time that you’re looking for, that the sun will last with the given energy density you mention, and mass. you’ll have to look up the luminosity, however.
this is wildly inaccurate, as you may have guessed, because the luminosity hasn’t always been constant, and obviously if you burn chemically the mass will change and so will the luminosity, yada yada yada, but to first order approximation, this is the method i believe you should use.
hope this helped.