Re: [Phys-l] PV question

[Brian Whatcott <betwys1@sbcglobal.net>]

John Mallinckrodt wrote:
> Brian Whatcott wrote:
>
>   
> > This reply is in haste:   a straight line on a P-V diagram would cross
> > isotherms unnecessarily - so cannot be reversible - at first blush....
> >     
>
> I'm not sure what you mean by "unnecessarily," but every process  
> other than an isothermal process crosses isotherms and there are  
> certainly reversible nonisothermal processes, so ... ?
>
> John Mallinckrodt
> Cal Poly Pomona
If a well insulated piston and cylinder is slowly squeezed, work enters 
the enclosed space as heating and pressure ride, with volume 
decrease.    If the process is perfectly reversible, when the piston is 
slowly released, the compressed gas returns work to the piston, and the 
initial values of pressure, volume, temperature and entropy are restored.

If I depict this process graphically, using a pressure volume  plot,  I 
start at some value of pressure and volume,  the initial temperature 
being represented by a point on an isotherm which is a curve. When the 
compression stroke is complete, I see a curved line crossing isotherm 
curves ONCE until the plot reaches a point on the high isotherm curve.

Because the form of the P.V function is a power (gamma) function of 
their product.
the  curve is asymptotic to P and V axes of course.

A reversible compression on a well insulated device of this kind (called 
in the jargon, a reversible adiabatic  process)  cuts any intermediate 
isotherm ONCE on its way to its peak temperature. The change in 
pressure, volume and temperature describes a curve of course.

If one specifies a straight line on such a PV graph, then the curve 
describing the pressure volume and temperature change during its 
compression  will necessarily cut some isotherm (actually many of them) 
TWICE.
The implication (for me) is that this straight line is not a description 
of a reversible adiabatic. process.

Brian W