Isentropic Processes: Pr and Vr

We can use this piece of information about a process to determine values of other properties of the system at either the initial or final states.
A process that is both internally reversible and

is

: .

2nd Gibbs Equation (Ideal Gas)

Now, consider a process from a reference state: Pref , Vref and Tref to any state P , V and T.
Notice that .

:

Relative Pressure

:
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Ch 7, Lesson E, Page 2 - Isentropic Processes: Pr and Vr

• I hope you remember that any process that is both internally reversible AND adiabatic is isentropic.
• ΔSwiggle is zero for an isentropic process and this lets us simplify the Gibbs Equations
• Now, let’s apply both of the ideal gas Gibbs Equations to an isentropic process that begins at the reference state that we chose for the ideal gas entropy function and proceeds to any arbitrary final state.
• Pref, Vref and Tref  are the properties of the reference state.  So is zero at the reference temperature.
• When we put all of this information back into the Gibbs Equations and do a tiny bit of algebra, we get the two equations in the gray boxes.
• Now, we define the relative properties.  The relative volume is the ratio of the actual molar volume of the system in the final state to the molar volume of the system at the reference state.
• Similarly, the relative pressure is the ratio of the actual pressure in the final state to the pressure at the reference state.
• These definitions convert the left-hand sides of the equations in the gray boxes into the natural log of Vr and the natural log of Pr, respectively.
• You can see that I put these equations in yellow boxes, so you’ve got to figure they are important or useful, right ?
• But HOW do we use them ?  Flip the page and let’s see.