[SivaRagu]

Hi,
What are the ways to demonstrate first law of Thermodynamics in an experiment?
Besides, the concept of Expansion.

Your ideas are welcomed and appreciated. Thank you

[Enthalpy]

Welcome, SivaRagu!

As a preamble, no experiment can demonstrate a law.

• A law is always valid, so you'd need to make all possible experiments with all possible values.
• The logic path (a demonstration) is from axioms to theorems and belongs to mathematics only.
• In experimental science, we go the opposite way, from observations to models which are not axioms. This is the inductive direction, not the deductive one. Consequently, a model can't be proven: it works often and well enough to please the scientists - until it's disproven or insufficient.
• That's not only rhetoric from me. Before the neutrino was proposed and much later observed, physicists observed that energy disappeared in the beta radioactivity, and accepted that from experiments.

Then, take the simpler case of mechanical work and electricity. You can convert 1MW electricity into movement and convert it back into >0.98MW electricity. Does that prove that you had nearly 1MW mechanical power meanwhile? No. Physicists observed that (...with worse efficiencies) often enough and decided that it would be convenient to call "energy" both electricity and work and use a single unit, and calibrated the electric measurement apparatus from the mechanical one. That's a model, nothing more. We could use horsepower*hours and faraday*volt*minute, and keep "work" distinct from "electricity", with some conversion factors known as best experimental limits.

The kinetic theory of gases, which models heat as other forms of energy like movement, and a bit later Quantum mechanics and Relativity, bring some new reasons to consider energy as something more general than electricity, work and so on - but at the time thermodynamics was modelled there was no such reason. So much that people long kept calories as the unit.

Worse, the first law has one more huge drawback: while we can convert anything into heat, we can't get back from heat all the energy that was dissipated. In the 19th century is was more like 1% work back. So telling "energy is conserved" from work to heat needed some cheek, and demanded immediately the second law to tell that getting all the work back was impossible. And as long as all heat engines had <10% efficiency, models could just equally well have told "work to heat is 10% efficient" and "heat to work is up to 100% efficient".

So with such experiments - probably the ones you can reproduce with limited effort - the first law is just one convenient convention. One reason to accept it would be if other forms of energy (work, electricity, chemical energy...) convert efficiently in an other, so telling "it's all energy" is a useful convention, and if they all convert into the same amount of heat, in which case "heat too is energy and we could use the same Joules" gets an interesting convention.

Based on that:

• Would a heat engine be a good choice if you thrive to make the first law look sensible?
• Or would you convert other energies in an other and into heat?
• Can you imagine a set of experiments that justify the choice of the first law?