How Much Mass Does the Sun Lose Each Day?

[verbose]

Homework Statement

The sun radiates energy at the rate of approximately 4 x 10^26 W. Assume that this energy is produced by a reaction whose net result is the fusion of 4 H nuclei to form 1 He nucleus, with the release of 25 MeV for each He nucleus formed.

Calculate the sun's loss of mass per day

Homework Equations

E = mc^2

The Attempt at a Solution

I think all the information about the Helium reaction is a red herring, but I'm
not sure. It's throwing me off. The problem says that the sun radiate energy
at the rate of 4x10^26 W, but it doesn't say in what time frame.
What I did at first, was assumed that that rate is per second and I did as follows;

1 day = 24 hours = 24*60 minutes = 24*60*60 seconds = 86400 s

Energy output in a day = 4x10^26 W/s * 86400s = 3.456 * 10^31 J

then I used E = mc^2 -> m = E/c^2 = 3.456 * 10^31 J/(2.0 * 10^8 m/s)^2
= 3.84 * 10^14 kg to be the amount of mass the sun loses every day.

Is this right, or do I have to use the given information about the Helium reaction?

 

[denverdoc]

I believe you are correct, its only asking for a mass equivalent of x amt of energy.

 

[m2003]

I would say that your initial approach is correct. The given information about the Helium reaction is not necessary in this calculation, as it is already accounted for in the rate of energy output from the sun. However, it is always good practice to double check and make sure that all relevant information has been considered in solving a problem. In this case, it seems that your calculation is accurate and you have correctly determined the sun's loss of mass per day. Well done!