# Lesson Overview

Integral form of the definition of

#### entropy

:
Goal:
Determine ΔS for reversible and irreversible processes for which complete thermodynamic tables are not available.
Steps:
1. Derive the 1st and 2nd Gibbs Equations that relate S to other state variables.

2. Apply the 1st and 2nd Gibbs Equations to processes in which the system is an incompressible substance and show how to evaluate ΔS for these processes.

3. Apply the 1st and 2nd Gibbs Equations to processes in which the system is an ideal gas and show how to evaluate ΔS for these processes. Three different methods are presented.

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### Ch 7, Lesson D, Page 1 - Lesson Overview

• In lesson B, we presented the definition of a new state variable or property and we called it entropy.
• Later in that same lesson, we saw that the NIST WebBook contains vast amounts of entropy data in its thermodynamic tables.
• Did you ever wonder how the scientists and engineers referenced in the WebBook managed to calculate values of S ?
• Well, I can tell you that they didn’t use the definition of entropy directly because internally reversible processes don’t exist.
• The way to calculate entropy from experimental data is to relate S to other state variables that are easier to measure, such as P, V and T.
• In this lesson, we will derive the 1st and 2nd Gibbs Equations.  These are the two key equations that relate S to other state variables.
• The research scientists and engineers used the Gibbs equations to help them calculate values of S from their experiments.
• OK.  That is great if we can find the entropy data that we need on the NIST website or in some other reference.  But, what do we do if we cannot find the data we need ?
• Well, in some cases we can make some approximations.
• Many liquids and most solids can be considered to be incompressible as long as the pressure doesn’t change by more than a MPa or two.
• We will apply the Gibbs Equations to the special case of incompressible substances and derive an equation we can use to calculate ΔS.
• Gases with a molar volume greater than 20 L/mole can be considered to be ideal gases.  For noble gases and diatomic gases the molar volume can be as low as 5 L/mole and we can still consider the gas to be ideal.
• So, we will apply the Gibbs Equations to ideal gases and derive equations to help us calculate ΔS.
• We will consider 3 different ways to solve these equations.
• By the end of the lesson, we will be as comfortable with determining ΔS for processes as we are with calculating ΔH.
• Alright.  Now that we know where we are going and why, let’s get started.