MHB Classical gases not necessarily ideal

  • Thread starter Thread starter Logan Land
  • Start date Start date
  • Tags Tags
    Classical Gases
AI Thread Summary
The discussion focuses on deriving a relationship between the pressures and volumes of classical gases in thermal equilibrium. Systems A, B, and C have the same number of molecules, and their pressures and volumes are measured. When A and B are in equilibrium, their relationship is expressed by an equation involving constants alpha, beta, and gamma. Similarly, a second equation relates A and C. To find the relationship between systems B and C, the key is to eliminate the common variable PaVa from the equations rather than directly equating them. This approach will yield a new relation between Pb, Vb, and Pc, Vc without the dependency on PaVa.
Logan Land
Messages
83
Reaction score
0
Systems A, B, and C are classical gases (not necessarily ideal), each with the same number of molecules N ( or same number of moles n if you prefer), where N is constant. We can measure pressures and volumes Pa,Va ; Pb,Vb ; and Pc,Vc for each system. When A and B are in thermal equilibrium, our measurements show that their pressure and volumes satisfy:
PbVb-(beta)Pb-(alpha)Vb+(alpha)(beta)-PaVa=0

When A and C are in thermal equilibrium, we find:
PcVc-PaVa-((gamma)PaVa)/Pc=0

where (alpha),(beta), and (gamma) are constants.
Find the equation relating Pb,Vb and Pc,Vc that is satisfied when system B and C are in thermal equilibrium.
Would I just set the equation for AB = AC and move the B and C's to one said and A to the other?
 
Mathematics news on Phys.org
LLand314 said:
Systems A, B, and C are classical gases (not necessarily ideal), each with the same number of molecules N ( or same number of moles n if you prefer), where N is constant. We can measure pressures and volumes Pa,Va ; Pb,Vb ; and Pc,Vc for each system. When A and B are in thermal equilibrium, our measurements show that their pressure and volumes satisfy:
PbVb-(beta)Pb-(alpha)Vb+(alpha)(beta)-PaVa=0

When A and C are in thermal equilibrium, we find:
PcVc-PaVa-((gamma)PaVa)/Pc=0

where (alpha),(beta), and (gamma) are constants.
Find the equation relating Pb,Vb and Pc,Vc that is satisfied when system B and C are in thermal equilibrium.
Would I just set the equation for AB = AC and move the B and C's to one said and A to the other?

Hi LLand314!

Not quite. Then you would still have an equation with Pa,Va in it.

The "trick" is to "eliminate" Pa,Va.

If you have for instance:
x-y=3
x-z=5
then you can "eliminate" x as follows.

We can rewrite the first equation as x=y+3.
Substitute that in the second equation to get (y+3)-z=5.
And now we have a relation between y and z, without x.

The same thing applies to your equation, where you should try to eliminate PaVa.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Back
Top