How could I define work and energy qualitatively without relating them to each other?
You know, I used to think energy was simply defined as some quantity that is able to be transformed into work. But somehow that doesn't seem to work when you confront it with the 2nd law of Thermodynamics (because then heat wouldn't be energy...), unless you'd allow a heat reservoir of 0K, but that doesn't really make sense.
No, that's actually the definition. Energy is the ability to do work.
And under perfect ideal circumstances, all heat can be converted to work. Second law mostly goes to the availability of these perfect ideal circumstances in the "real world".
But the ability to do work is still there.
K^2, with "under perfect ideal circumstances", do you mean like the demon of Maxwell? In that sense I agree. But then I suppose calling heat energy is dependent on the atomic theory? (because in (macroscopic) thermodynamics itself I don't think you can ever put Q into W, right?)
No, an ideal gas placed in perfectly thermally isolated cylinder with nothing on the outside and allowed to do work against a piston would exhaust all of its internal energy by the time the volume infinitely expands. Problem is allowing for infinite expansion, perfect insulation, and zero external pressure.
You didn't say what your interest is. Are you a teacher, if so there is another thread discussing something similar.
It cannot exhaust all its energy, I thin it was proven that even at absolute zero there is the zero point energy.
Also you cannot talk about infinite expansion since the molecules will be traveling too slowly as they approach absolute zero. Then there is the problem with low pressure analysis where if you only have a few molecule collisions against the "piston" it will be impossible to collect the energy. The ratchet engine was proven to not work for this reason.
You can destroy the ability to do work, even a simple example of the free expansion of a gas shows this.
Curl, do you then have any idea how Q is argued to be energy if the definition of the latter requires being able to be "transformed" into work?
I don't understand your question. Q is generally a symbol for heat, which is defined as thermal energy transfer. Having non-zero thermal energy does not mean that work can be done by that system.
Consider a closed system with nonzero temperature. Inside that closed system there can or cannot be the ability to do work. It depends if there is a temperature differential. Even if there is, the system can undergo energy transfer and the temperature of each object will reach equilibrium in which case the ability of the closed system to do work has vanished.
Zero Point Energy has to do with Quantum. There, Energy is defined completely different. Stick to classical mechanics for this.
In classical mechanics, 100% of body's heat can be converted to mechanical work under right conditions.
Still wrong because "right conditions" are not possible and its not because of engineering difficulties. Every closed system can lose its ability to do work (relative to itself) although every closed system cannot lose energy. See my post above.
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