4.1: Prelude to Putting the First Law to Work Because thermodynamics is kind enough to deal in a number of state variables, the functions that define how those variable change must behave according to some very well determined mathematics. This is the true power of thermodynamics! 4.2: Total and Exact Differentials Total differentials are used identify how a change in a property depends on the changes of the natural variables of that property. 4.3: Compressibility and Expansivity A very important property of a substance is how compressible it is. Gases are very compressible, so when subjected to high pressures, their volumes decrease significantly (think Boyle’s Law!) Solids and liquids however are not as compressible. However, they are not entirely uncompressible! High pressure will lead to a decrease in volume, even if it is only slight. And, of course, different substances are more compressible than others. 4.4: The Joule Experiment Joule's experiment concluded that dq=0 (and dT=0) when a gas is expanded against a vacuum. And because dV>0 for the gas that underwent the expansion into an open space, the internal pressure must also be zero! 4.5: The Joule-Thomson Effect Joule and Thomson conducted an experiment in which they pumped gas at a steady rate through a lead pipe that was cinched to create a construction. A cooling was observed as the gas expanded from a high pressure region to a lower pressure region was extremely important and lead to a common design of modern refrigerators. Not all gases undergo a cooling effect upon expansion. 4.6: Useful Definitions and Relationships Several useful definitions have been stated that connect partial derivatives to experimental measurements. Together, these relationships and definitions make a powerful set of tools that can be used to derive a number of very useful expressions. 4.E: Putting the First Law to Work (Exercises) Exercises for Chapter 4 "Putting the First Law to Work" in Fleming's Physical Chemistry Textmap. 4.S: Putting the First Law to Work (Summary) Summary for Chapter 4 "Putting the First Law to Work" in Fleming's Physical Chemistry Textmap.