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Entropy & Second Law of Thermodynamics: Nuts & Bolts

Entropy & Second Law of Thermodynamics: Nuts & Bolts

3. Nuts & Bolts

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Multiple Representations

Multiple Representations is the idea that a physical phenomena can be explored in many different ways. For example, there is the physical representation which models the system with figures and diagrams, such as a free body diagram. There is also the mathematical representation which uses the equation(s) governing the physics of the system. All of the representations can be used together to help us understand and quantify the physical phenomena.

Observe the different types of representations for this section below:

Physical Representation

Physical Representations explain the features of the situation in a visual way, often with vector representations of physical quantities overlaid a simple diagram or picture of the situation.

We have a system with a moveable wall. Once the wall is removed, the particles move toward a new equilirium.

Mathematical Representation

Mathematical Representation uses equation(s) to describe the situation.

$*Q = \lim_{\Delta S \to 0} \sum T \Delta S $  

*Actual equation not important.What is important is that conceptually heat is proportional to the change in entropy.

Conceptually, heat (Q) is from $\Delta S$

Graphical Representation

Graphical Representation describes the situation through use of plots and graphs.

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Descriptive Representation

Descriptive Representation is made up entirely of words or annotations. Think about how you might explain the situation to someone else.

Entropy drives isolated systems, such as the boxes of particles shown in the Physical Representation, to increased disorder. Where more disorder has larger micro multiplicity and a larger multiplicity means more microscopic configurations with the same macroscopic observables such temperature (T), pressure (P), $E_{th}$, etc...

Experimental Representation

Experimental Representation could be thought of as doing the experiment.

 

We can design an experiment by taking a water filled ballon and popping it. Initially, the water in the balloon is contained and relatively uniform. However, as soon as we pop the balloon the water molecules become scattered and begin to spread out to form a new equilibrium. 

 

Example Problems

For additional practice problems and worked examples, visit the link below.