Use the luminosity of the sun, the total amount of energy it emits each second, to calculate how much mass it?

Question

converts to energy each second.

Answer 1

well what is the luminosity and energy emission?

Answer 2

Well, this is interesting, but I'm not sure how much I can help.

There is a generally recognized relationship between the luminosity of a star and its mass, based on hydrostatic equilibrium and the sensitivity of nuclear reactions to the ambient temperature, but the theory isn't well-developed enough to compute all the parameters so people have been using observations. Here are two sites, one setting the exponent at 3.5 and the other at 3.9:
http://zebu.uoregon.edu/~imamura/208/jan23/ml.html
http://csep10.phys.utk.edu/astr162/lect/binaries/masslum.html

The second also shows that, as with all empirical derivations, there are exceptions.

Here is an overview:
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit2/structure.html

Here is how far simple theory will get you:
http://zebu.uoregon.edu/~imamura/208/feb6/mass.html

With respect to your original question, there is one problem with all of these - all the equations ar in terms of solar masses and solar luminosities. So in the case of our Sun, rather than an arbitrary star, its luminosity of one solar luminosity give a mass of one solar mass.

Hope this helps, sorry I can't give you more.