Re: [Phys-l] T dS versus dQ

[Brian Whatcott <betwys1@sbcglobal.net>]

I am getting an uneasy sensation from reading your modeling of the work 
input
to rapid compression, John.   It reminds me too strongly of the folks
(former Physics students, I can suppose?) who model aerodynamic effects
like lift in terms of physics-type billiard balls impacting.

If one asks how does that effect the flow curvature that is noted
well-ahead of a wing in flight, the responses grow labored.

I venture to believe that there are emergent properties of fluids that
occur on much larger scales than the molecule.

When Dr Reynolds modeled the flow of water in gutters, he had no cause
to go to any considerable fraction of the speed of sound in water at all.
Other properties controlled the turbulence that he saw developing at
rather low water speeds. Could it be that a model might include other
turbulent influences on snap compressions?

Brian W


John Mallinckrodt wrote:
> Carl's note along with a hint from bc's recent message prompt me to  
> suggest a model for very rapid compression in which work is done  
> against the initial pressure, P_o, plus a dynamic pressure given by  
> (1/2) rho_o (2v)^2 where v is the piston velocity and 2v is the  
> velocity to which the impacted gas is accelerated.
>
> If we express v in terms of a dimensionless fraction of the rms speed  
> of the gas molecules, i.e., v = alpha*v_rms = alpha * sqrt(3*P_o/ 
> rho_o) then the first law
>
> E_f  =  E_o  +  W
>
> becomes
>
> (f/2)nRT_f = (f/2)nRT_o + (P_o + 6 alpha^2 P_o)* | delta_V |
>
> where f is the number of degrees of freedom for the gas. /snip/
>   

> John Mallinckrodt
> Cal Poly Pomona
>
> Carl Mungan wrote:
>
>   
> > I think there's no practical problem with the Adiabatic Gas Law
> > apparatus. /snip/