# 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.
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