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This question is about whether the mass of a particle increases with its speed. Here is my related question from which this question spawned: Why is there a controversy on whether mass increases with speed?

Imagine I've got a lump of matter with a fixed number of atoms. I take this into a region of space where there is no gravitational field strength. I apply a force to it, measure its acceleration, and then calculate its mass.

I then heat the matter up, and perform the same experiment again.

Will I measure a different mass?

Why/ why not?

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User 17670
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  • I'm not sure what relevance the acceleration has to your question. In short though: yes, heating up an object increases its mass. – lemon Sep 06 '14 at 14:00
  • Yes, you would measure a different mass, but the direct measurement would be very difficult. – CuriousOne Sep 06 '14 at 14:04
  • Can I have an explanation? Also, this is just a thought experiment, so we're assuming that all measurements are as accurate as nature lets them be. – User 17670 Sep 06 '14 at 14:12
  • @User17670: What kind of explanation are you looking for? That energy and mass are equivalent has been experimentally tested, just not for small amounts of heat. That is, if you wish, an extrapolation. As to the "controversy" over the mass increase with speed, that's less of a controversy, than a failure to understand the difference between coordinate systems in relativity by some. – CuriousOne Sep 06 '14 at 15:01

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This is exactly the source of energy exploited by the fission of high-mass nuclei (i.e. nuclear power).

You start with a heavy nucleus (say $^{235}\mathrm{U}$) and add a neutron. What you get out is two lighter nuclei (often, but not always, krypton-92 and barrium-141) and several neutrons: $$ ^{235}\mathrm{U} + n \to ^{92}\mathrm{Kr} ^{141}\mathrm{Ba} + n + n + n \,.$$ The mass of all of these bits can be measured to high precision, and the mass of the reactants is larger than the mass of the products.

The differences is that there is more internal energy in the uranium than the total internal energy in the krypton and barium.

The extra energy shows up as kinetic energy (mostly of the product neutrons) and is converted to thermal energy in the moderator, used to heat water, which runs a turbine and powers your iphone (or what every).

Short-short answer: Yes, internal energy is mass (though you need the factor of $c^2$ to put it in units of kilograms).

Aside (on account of your previous question): No, that doesn't mean that it is better to talk about "relativistic mass" because internal energy includes binding as well as motion. It just means that the mass of a composite system is not necessarily the same as the mass of it's constituents.

Homework: Determine how much mass 1 kilogram of water gains when heated (at STP) from freezing to boiling.

dmckee --- ex-moderator kitten
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