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Lesson Overview

In the previous lesson, we derived the following two forms of the 1st and 2nd

Gibbs Equations

for ideal gases.

1st Gibbs Equation (Ideal Gas)

2nd Gibbs Equation (Ideal Gas)

In this lesson, we will apply these equations to

isentropic

processes. This will lead us to define the

relative volume

and

relative pressure

, Vr and Pr. These functions are tabulated along with So in the

Ideal Gas Entropy Tables

for some common gases.

Then, we will consider special

isentropic

processes in which the

heat capacities

of our ideal gases are constant. This will lead to three helpful relationships between P, V and T.

Finally, we turn our attention to

polytropic

processes. These processes can include

irreversible

processes as well as systems that contain real fluids as well as ideal gases. We will find that an

isentropic

process on an ideal gas with constant heat capacities is a special case of the more general

polytropic

process. We will also see that

isothermal

isobaric

and

isochoric

processes can also be considered to be special cases of the

polytropic

process.

Lesson
7E Blog

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Lesson 7E: page 1 of 22

Previous LESSON

Our big achievement in the last lesson was the derivation of the 1st two Gibbs Equations.
The forms of the 1st and 2nd Gibbs Equations shown here apply only to ideal gases.
In this lesson we are going to see what we can learn from these equations when we apply them to isentropic processes.
This analysis will lead us to the concepts of relative pressure and volume.
Don’t get these confused with the reduced pressure and reduced volume that we discussed back in chapter 2 when were learning about the generalized compressibility charts.
Next, we will look at a special case within isentropic processes with ideal gases. We will consider processes in which the heat capacities of our ideal gases remain constant.
This will yield three sweet little equations relating P, V and T. These equations make the analysis of such processes pretty straightforward.
That is what you would expect. The more simplifying assumptions you make, the easier the analysis should be, right ? The other side of the coin is that fewer processes can be accurately described by the simpler model.
Finally, we make the key observation that ties this lesson together.
An isentropic process using an ideal gas with constant heat capacities turns out to be a special case of a more general type of process called a polytropic process.
Polytropic process can be reversible or irreversible. They can use ideal gases or real fluids. Heat capacities can be constant or not.
The cool part is that most of the types of processes that we have discussed in this course so far can be considered to be special cases of the general polytropic process.
For example, isothermal, isobaric and isochoric processes are all polytropic processes as well.
As a result, we can learn how to apply the 1st two Gibbs Equations to all of these types of processes by just learning how to apply them to the general polytropic process.
Well, as you may have guessed, this is going to be a long lesson. So, we had best get started.

Lesson Overview

Gibbs Equations

1st Gibbs Equation (Ideal Gas)

2nd Gibbs Equation (Ideal Gas)

isentropic

relative volume

relative pressure

Ideal Gas Entropy Tables

isentropic

heat capacities

polytropic

irreversible

isentropic

polytropic

isothermal

isobaric

isochoric

polytropic

Ch 7, Lesson E, Page 1 - Lesson Overview