@jh It's the quantity that is conserved because (as far as we know) the laws of physics are the same at different points in time =)

[that's probably not too helpful either, and I'll check back in a bit to see if someone posts a helpful definition -- if not, I'll think and try to expand on the above]

@jh
1/n Ack! I'm not sure how well I can do this (I keep rediscovering that I am not a very good physicist), but let's try

First.. I don't think the definition "energy is the capacity for doing work" is very good. For example, what exactly does capacity mean in this context? If we let the universe evolve forever and it reaches "heat death" (https://en.wikipedia.org/wiki/Heat_death_of_the_universe), the soup that is our sad end-state universe will certainly have some energy, but that energy won't have the "capacity to do work"

@jh
2/n I don't think it's easy to write down a snappy, universal, and useful definition of 'energy', because it appears in different fields in different ways

Energy is some quantity that turns out to be conserved, but takes many forms -- and these forms can be converted from one to the other (and therefore all have the same unit -- the Joule)

@jh
3/n For example, you can convert kinetic energy (1/2 * mass * velocity^2) into gravitational potential energy (mass * g * height) by throwing a ball onto a roof. When the ball later falls from the roof, it first converts that gravitational potential energy into kinetic energy, and then when it stops moving, the energy is converted into thermal energy (the temperature of the ball and the ground increases).

Incidentally, thermal energy is really kinetic energy on the molecular scale

@jh
4/4
I looked around for some article that describes this better than I can, and this chapter from Feynman's lecture is what I found: https://www.feynmanlectures.caltech.edu/I_04.html

Which brings is back to this "the capacity for doing work" thing. To me that sounds more like the definition of "free energy" than just "energy": https://en.wikipedia.org/wiki/Thermodynamic_free_energy