# Mass to energy conversion in living beings

I have a doubt regarding mass to energy conversion. Suppose I consume m1 kg of food at beginning of a day. Will it be equal to the mass of solid and liquid wastes out of my body on that day (say m2) and increase in mass of my body (say m3) and added to energy gained by me from that food (Eg) according to famous relation $E=mc^{2}$ (Let us assume initial conditions of my body to be zero). That is
$$m1=m2+m3 + \frac{Eg}{c^2}$$.
Since a small difference in mass (Mdiff=m1-(m2+m3)) is equivalent to enormous amount of energy, and by my common sense (which may be wrong) I feel Mdiff will be significant leading to energy gained Eg to be very high, I doubt the mass-energy equation.

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Borek
Mentor
That's the problem with E=mc2, conversion factor (c2) is so large it makes is almost impossible to observe mass changes in the surrounding reality. But it doesn't make E=mc2 wrong, just impossible to observe in everydays life.

That's not the only thing that is hard to believe using just a common sense, time dilation or tunneling effect also don't make sense when you try to understand them using intuition trained to deal with low speed macroscopic objects. Does it make these effects wrong? No, just more interesting

russ_watters
Mentor
Because of this, that equation really only works well for nuclear reactions. Not for chemical reactions.

Dale
Mentor
2020 Award
Also, in your equation you missed mass lost due to breathing. Exercise doesn't really have much impact on urine or feces production. So when you exercise to lose weight you lose it chiefly in two ways:
1) sweating - water and electrolytes, replaced upon drinking
2) breathing - water and CO2, the water is replaced upon drinking and the CO2 represents the real weight loss

Because of this, that equation really only works well for nuclear reactions. Not for chemical reactions.

Are you sure about that? A water molecule does not have the same mass as 2 H's + 1 O, does it?

Borek
Mentor
Russ stated "it only works well" - by which I suppose he meant that this equations can be easily used to calculate amount of energy liberated in nuclear reactions, but in other cases using it is a waste of time (even if technically correct).

Are you sure about that? A water molecule does not have the same mass as 2 H's + 1 O, does it?

Sure it does, not including relativistic effects.

gmax137
By 'working well' I think we mean, 'we can measure the calculated change in mass.' Since c^2 is so big, the changes in mass associated with chemical reactions are tiny, where 'tiny' means they can't be measured with normal equipment.

Yes, of course the H2O molecule weighs less than the individual atoms - but I doubt you have a scale that can make that determination. And that's why the relationship (mass to energy) remained undiscovered for so long. And also why it was discovered by a guy with a pencil, rather than by someone in a lab coat.

Andy Resnick
I have a doubt regarding mass to energy conversion. Suppose I consume m1 kg of food at beginning of a day. Will it be equal to the mass of solid and liquid wastes out of my body on that day (say m2) and increase in mass of my body (say m3) and added to energy gained by me from that food (Eg) according to famous relation $E=mc^{2}$ (Let us assume initial conditions of my body to be zero). That is
$$m1=m2+m3 + \frac{Eg}{c^2}$$.
Since a small difference in mass (Mdiff=m1-(m2+m3)) is equivalent to enormous amount of energy, and by my common sense (which may be wrong) I feel Mdiff will be significant leading to energy gained Eg to be very high, I doubt the mass-energy equation.

This is a totally inappropriate approach. Humans consume about 2 kCal/day- figure out the mass equivalent from that.

See my post #3 in