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Re: [Phys-l] PV question

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