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I had an argument with someone.

I argued that when a cat eats 1 kg of food, the sum of subsequent output (poo + pee + sweat + change of body mass) must be equal to 1 kg.

My opponent argued that the output will be less than 1 kg because a part of food is converted into energy.

Please rule.

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    $\begingroup$ Possible duplicate: biology.stackexchange.com/questions/73288/… $\endgroup$ – Bryan Krause Aug 1 at 18:02
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    $\begingroup$ Possible duplicate of When you lose weight, how does the mass exit your body? $\endgroup$ – David Aug 1 at 18:06
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    $\begingroup$ So your opponent is claiming that your cat is a nuclear reactor? One thing you're neglecting here is that a portion of the mass of the food will leave as CO2. $\endgroup$ – jamesqf Aug 1 at 18:23
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    $\begingroup$ This is NOT a duplicate of When you lose weight, how does the mass exit your body? because that question explicitly says 'And please, don't suggest that it was "converted to energy"' and the answer avoids that aspect, while the present question explicitly asks about conversion into energy. The answers are different from the point of view of a biologist or chemist versus that of a physicist. $\endgroup$ – mgkrebbs Aug 1 at 19:13
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    $\begingroup$ During metabolism, the energy is released from the chemical bonds, while the atoms and their atomic mass and therefore the mass of everything what a cat eats and excretes remains the same. $\endgroup$ – Jan Aug 2 at 10:05
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Physics answer that is a bit silly

If you want to be real technical about physics, mass and energy are the same thing, so any chemical bond that has some energy and is broken results in a change of mass (mgkrebb's estimated in a comment the final mass would be 999.999999814 g, if you started with 1 kg of protein, also known to a very precise biologist as 1.000 kg).

This is sort of a "technically correct" answer that is totally silly from the standpoint of biology, but if your opponent wants to stand by it as "technically correct" based on physics, so be it. We are talking about changes in mass that are not measurable by modern science to sufficient precision, these are only theoretical ideas based on relationships between mass and energy that can be measured on a much larger scale.

Biology answer

Since this is Biology.SE, the biology answer is that mass is conserved in chemical reactions. If you greatly simplify the metabolism of, say, glucose, to the equation:

C6H12O6 + 6 O2 --> 6 CO2 + 6 H2O

you find that the net result is that the hydrogen and oxygen atoms become water, and the carbon atoms become part of carbon dioxide (yes I am simplifying where the actual atoms end up in the biochemical reactions, just talking in terms of net changes here). Other food molecules are processed similarly, and will produce some combination of water/carbon dioxide/nitrogenous wastes. If your cat eats 1 kg of food, that 1 kg of food will become 1 kg of something else out to many many decimal places: waste solids (including anything not digested at all) and liquids, exhaled carbon dioxide, lost skin/hair, etc.

Physics answer if you just want to win the argument

If you want to still win the argument with the physics-based answer that relies on mass-energy equivalence and ignores the fact that from the perspective of biology they are best understood as different concepts, then it's just as fair to go the other way and treat the lost energy as mass, in which case you'd consider the heat lost by the cat's metabolism as mass and include that tiny tiny tiny fraction in the 1 kg and call it a day.

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    $\begingroup$ I wouldn't characterize the most precise accepted scientific description as "a bit silly", but the resulting mass deficit is at present immeasurable. If you feed the cat 1 kg of protein and it was entirely metabolized, it would release about 4000 kcal of energy, equivalent to 1.862e-7 g of mass. This means the products from the 1000 grams of food would not conserve all their mass, but instead have a mass of "only" 999.999999814 grams. $\endgroup$ – mgkrebbs Aug 2 at 21:06
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    $\begingroup$ @mgkrebbs From a biological perspective, measures out to 10-12 significant digits are, in fact, silly. Just as silly as using relativity when a physical system is within the bounds of Newtonian mechanics. There are too many sources of variation and error to give measurements of that precision any meaning. It doesn't make the physics wrong or not precise, of course, but chemists and biologists don't worry about those differences. Neither do physicists in most contexts. $\endgroup$ – Bryan Krause Aug 2 at 21:19
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    $\begingroup$ @BryanKrause, I agree that there is no practical importance to the mass change since it is immeasurable, and therefore it should be dismissed for thinking about most problems since it adds useless detail when considering how most things work. For arguments and wagering, however, the immeasurable details do matter. $\endgroup$ – mgkrebbs Aug 2 at 21:28
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    $\begingroup$ Love this answer +1 $\endgroup$ – AliceD Aug 2 at 21:42
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    $\begingroup$ @mgkrebbs Fair enough. I'll add your number to my answer if you don't mind because I do think it's useful. $\endgroup$ – Bryan Krause Aug 2 at 21:47
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Your opponent is correct. Some mass transforms to energy; the amount is negligible. One good source

If you and your friend decide to do an experiment in a controlled environment and measure the masses with a scientific scale with the highest precision available today, you will see that the total mass at the beginning of the experiment and the total mass at the end are same. Because, the scale isn't precise enough to measure very very small amounts of mass.

But, this won't mean that your opponent is wrong. Because, in terms of physical laws, there will be a very small amount of change in the total mass which is the source of the energy that will be released in metabolism in various kinds like heat.

This physics.stackexchange thread can be helpful to understand the physical nature of the event..

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  • $\begingroup$ We are looking for more extensive answers explaining the topic. You just quote someone making an assertion without any evidence behind it. What is needed to support your argument is a calculation showing how much mass is converted into energy in a specific chemical reaction. Can you provide this? $\endgroup$ – David Aug 2 at 17:22
  • $\begingroup$ No I can't provide a calculation and this would be unnecessary as it isn't the question. $\endgroup$ – Harun Aug 2 at 18:53
  • $\begingroup$ Hardin, I am trying to help you understand how this site works. @Bryan Krause has supplied just such an answer. Please read the Help on Answering Questions. $\endgroup$ – David Aug 2 at 18:58
  • $\begingroup$ Edited my answer. Hope this helps. $\endgroup$ – Harun Aug 2 at 19:05

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