# Can doing positive work in a system add mass to it?

We know that doing work changes the internal energy of a system. If we transfer energy in the form of work to an isolated system, we cause a change, an increase in the internal energy.

1. Work is force times displacement and force is mass times acceleration. Assuming that we prevent any acceleration, could there be a change in mass?

2. Work is a form of energy and as Einstein proved energy-mass equivalence $$E=mc^2$$, could the form of energy added by work be converted to matter? If yes, then please specify the conditions for the same to happen.

• Generally speaking, the answer is yes. But your point 1 assumes Newtonian mechanics, whereas point 2 - the relativistic one. Commented Mar 15, 2023 at 13:59
• Consider heavy element fusion.
– g s
Commented Mar 15, 2023 at 20:22

I am not actually sure about what are you trying to ask in the first part of your question. Maybe in future you will clarify about this more clearly, But for now, surely I can answer the second part of it.

And the answer is yes and no both, it is Yes in the case if that thing really matters for you i.e if you are doing some of the experiments in which the minute changes in mass will affect the whole situation and also in the case if you are working on something big like you are doing an enormously huge workdone on your system.

And the answer which includes No is when you are not working on any experiments which involves extreme amount of workdone, then that won't really matter.

Now let's come on to the reason behind this, the reason is that the term $$C$$ in the equation $$E=mC^2$$, is speed of light and that has really a big number! And if you square that then it will become tremendously huge. And if you divide the amount of work you are performing on your system (considering it as a small number) by this huge $$C^2$$ then that will truly come out to be a very small value for change in mass which will really not affect your experiment. But if the amount of workdone is so huge then you will have to take care of this while performing your experiment.

• Hmm. taking example of a battery, we charge it from wall adapter the charger gives it electrical potential energy, but doing so does not seem to affect its mass, or does it? Commented Mar 15, 2023 at 14:33
• @user18398875 where ever you get term 'Energy' it definitely has some mass associated with it, so it does affect the mass of that battery you are charging. But that is too small that it really won't affect your everyday life. Commented Mar 15, 2023 at 15:20
• @user18398875 Google Calculator can show you how tiny the mass is, eg Commented Mar 15, 2023 at 17:19

Yes, In an endothermic reaction let's say, it isn't reversible, the reactant $$A$$ absorbs heat and becomes products $$B$$ and $$C$$ and If you manage to put the reactant on one side of a scale and the products on the other side of the scale, you will see $$B+C$$ will weigh more than $$A$$.