What term to use, when the theoretical solution is absolutely inapplicable in practice due to other outstanding factors?

Let me give an example from my answer to Is there a maximum Isp for “exothermic chemical reaction rockets”?.

The most energetic reaction seems to be (although the claim is unsourced) oxidation of beryllium At 23.9MJ/kg it would purely theoretically allow 705 seconds of specific impulse. Purely theoretically, because beryllium oxide is a powder, so there's no adiabatic expansion of gas which creates propulsion.

And the comment by Uhoh:

I wish we had a better word than "theoretically" here. I can't think of one, but it's really just an absolute upper limit. Well know, unavoidable thermodynamic realities will probably lead to a lower number without question, so there's no actual "theory" that says it can be 705. But ya people frequently use "theoretically" like this.

I agree with the comment; the qualifier "purely theoretically" is clumsy here. The theoretical rule (all chemical energy converted to kinetic) simply doesn't apply in this case (the mechanism of conversion of chemical to kinetic energy doesn't work if the product of reaction is not a gas). Is there a better way to formulate the qualifier that 'this will not work in practice due to unrelated reasons'?

  • In theory: according to a theory; theoretically. - idioms.thefreedictionary.com/in+theory
    – user66974
    Oct 13 '16 at 9:07
  • 1
    Yes, 'theoretical' etc are used in this sense, and are woefully ambiguous in this register. I think you may be stuck with 'From purely energetics considerations, an upper limit of ...' etc. Oct 13 '16 at 9:08
  • @JOSH: The problem is that it doesn't really say about whether 'In practice' or not. Usually it implies the practical solution may be a bit short of the theoretical one, but not very far (the practical use of LH2/LO2 fuel results in 86% of the theoretical performance cap). In this case I need to emphasize the theory doesn't approximate the real results within any acceptable error margin.
    – SF.
    Oct 13 '16 at 9:26
  • What about...it would not realistically allow 705 seconds...
    – user66974
    Oct 13 '16 at 9:30
  • 'hypothetically'?
    – Spagirl
    Oct 13 '16 at 9:33

"According to the simplest model" would probably work in an academic context, although it would just be confusing in general popular writing. It would be appropriate because most 'theoretcal' statements of this type are based on mathematical models of one sort or another.

Using this would turn the posted extract into "According to the simplest model it would allow 705 seconds ... However this model does not apply because beryllium oxide is a powder..."

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