Does converting chemical bond energy into kinetic energy somehow remove energy (i.e. mass) from the system?
Does a block at rest sitting on the top of a hill have more mass than a spinning block at the bottom of a hill (assuming the rotational kinetic energy equals the difference in potential energy)?
Whether the energy leaves a system depends on the particulars. If you burn some hydrogen in a bomb calorimeter, the energy will stay inside the calorimeter. This is a "closed system". If you burn it with an open flame, the kinetic energy will warm the atmosphere. This is an "open system". The energy could end up anywhere... you can use hydrogen to launch rockets into space.
Since the energy can end up anywhere and the energy has mass, the mass can end up anywhere, too.
I don't follow how that explains why two identical objects with the same energy content should be expected to have different masses. It seems like this whole thread is trying to argue that chemical reactions destroy mass through examples of open systems that leak energy. A leaky water balloon loses mass, too but that doesn't constitute evidence that atmospheric pressure/tension/etc destroys mass, does it?
If you take a block of steel from the top of a hill to the bottom of the hill and convert all the potential energy to kinetic energy (without loss), why would the mass of the block be altered? It may well be true, but arguments based on applying the mass-energy equivalence is not the answer.
Likewise, if you start with some pool of molecules and rearrange the constituent atoms and bonds, energy must be balanced via kinetics (i.e. translational and rotational energy of and within molecules on both sides of the reaction)--why should anyone expect the overall mass to change from such chemical reactions?
This is only approximately true. It would be hard to measure the difference, for sure. Relativity gives a lot of seemingly bizarre results:
* If you carry something uphill, it gains mass as you go. (Kind of... consider that it is part of a system which includes the Earth.)
* If you compress a spring, it gains mass.
* If you charge a battery, it gains mass.
* If you fire a laser into space, it will have a longer wavelength when it gets there.
* If you hook a shaft from the ground into space and turn it, it will turn faster at the bottom and slower at the top.
We live in the "middle ground" which is well approximated by Newton's laws. Strictly speaking, Newton's laws are false.