About math and science

[Elessar]

I was cleaning out my external HDD to make room for the Star Trek that's gonna go with me to the con when I found my report on the thermodynamic properties of the freon gas R-134a and their applications to liquid-vapor propulsion in a microsatellite, and I found that I actually had provided in the index a proof that temperature of a fixed-volume gas goes down as internal mass goes down. It's common sense for anyone who has used a can of air duster to clean their computer but I wanted to prove it, because we were submitting this to NASA, so I did. It's a really simply proof but I was proud of it because thinking back to my whole college career in mathematics, it was probably one of the most indepedent mathematical proofs I ever performed, starting out with nothing given to me, just a problem and a few assumptions. check it out...

Mathematical Proof that Expulsion of Propellant Causes Temperature Decrease
Basis : as we expel mass, the mass component Mg goes down, and so does mass fraction. Beginning with three assumptions:
• Definition of Mass Fraction is valid : x = yg / yg+yf, where y is a state property such as internal energy. This is the basis for linear interpolation and is valid.
• Definition of Internal Energy says U is proportional to T : U = u(T)
• Relation of Specific Internal Energy: U = Mu.

1. Mu=U
2. MT[uf + x(ug-uf)] = U
3. x = Mg/Mg+Mf ჻ (Mg+Mf) [uf +(Mg/Mg+Mf)(ug-uf)]
4. (Mg+Mf)uf + [(Mg+Mf)/(Mg+Mf)] Mgug - [(Mg+Mf)/(Mg+Mf)] Mguf
5. (Mg+Mf)uf + Mgug – Mguf = U
6. mf→constant, uf→constant, ug→constant, ჻ (ug-uf) →constant.
7. (Mg+A)B + Mg( C ) = U
8. BMg + AB + MgC = U
9. Mg(B+C) +AB = U

჻Since Mg↓ as X↓, and A, B, C are all constants, the sums and products (B+C) and AB are also constant. Therefore if Mg↓, so must U. And U is proportional to T,

჻ Mg↓ ჻ U ↓ ჻ T↓.


NOTE: Sorry, the subscripts don't show up as subscripts. Any variable like "Mg" is supposed to be M with a subscript g to indicate "Mass of gas", or "MT" meaning... I forget Total Mass maybe. Oh and the three-dots means 'therefore'.

[Asso]

[Bookworm]

It's a really simply proof but I was proud of it because thinking back to my whole college career in mathematics, it was probably one of the most indepedent mathematical proofs I ever performed, starting out with nothing given to me, just a problem and a few assumptions. check it out...

I think it's the one of the best feelings in the world, when you manage to solve a problem by yourself. And I just hate it when I can't come up with an answer or have to ask someone else do a proof for me.

Right now I'm really stuck with a problem in measure theory. I'd like to proof for myself that we can find all sets that are measurable with Caratheodory condition. I know and understand the proof that we can find measurable sets with it, but does it define ALL measurable sets.

[Elessar]

It's a really simply proof but I was proud of it because thinking back to my whole college career in mathematics, it was probably one of the most indepedent mathematical proofs I ever performed, starting out with nothing given to me, just a problem and a few assumptions. check it out...

I think it's the one of the best feelings in the world, when you manage to solve a problem by yourself. And I just hate it when I can't come up with an answer or have to ask someone else do a proof for me.

Right now I'm really stuck with a problem in measure theory. I'd like to proof for myself that we can find all sets that are measurable with Caratheodory condition. I know and understand the proof that we can find measurable sets with it, but does it define ALL measurable sets.

=! a guy who knows anything about measure theory