# 1.6: Looking Back and Ahead

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- 2056

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Let’s reflect on what we have done in the course up to this point. Our focus has been on developing an energy model, which we’ve called the *Energy-Interaction Model*, and on understanding how to apply it to some particular thermal phenomena. We have used this model to begin to understand some of the more general thermal properties of matter. We will continue to develop the *Energy-Interaction Model* as we apply it to new kinds of phenomena in Chapter 2.

Let’s think about how we have used the *Energy-Interaction Model* so far. If we included all energy systems that were involved in the process or interaction, we had a closed system and modeled the physical system as being composed of several energy-systems, each of which might exchange energy with one or more of the other energy-systems within the closed system. So, to make headway with this approach, we had to be able to identify relevant energy-systems. So far, we have considered bond and thermal systems explicitly. If we thought of the physical system as being an open system, then in addition to exchanges of energy among the energy systems within the physical system, we allow for the possibility of energy entering (or leaving) the system.

The next step is to add additional energy-systems to our repertoire, so we can handle other types of phenomena with different kinds of interactions. Fortunately, there are not that many different energy-systems. So, after we have added just a few more, we will be in a position to tackle questions about many more phenomena than we could even deal with in one quarter or semester. But that is precisely the power of this approach. It is so universal that you don’t need to be shown how to use it for each different phenomenon. Once you are comfortable with the approach, it becomes your own powerful tool, which you can use anytime you need it.

What have we left out in what we have done so far? Think back over all of the phenomena we have discussed and the questions we can answer with this approach. Basically, we can get at the values of quantities, or more precisely the changes in these values that occur as a result of the interaction, but we can’t get information about the details of the interaction or what goes on during the interaction.

When we want to know something about the details of an interaction or the dynamics of the phenomenon, we will need to use an approach, or model, that incorporates these details. But precisely because we have to incorporate more detail, the models will not be nearly so general as the *Energy-Interaction Model*. In Part 2 of the course we will devote considerable effort to understanding the Newtonian model, which allows us to very accurately calculate motions of objects. In Part 3 we focus on a very useful wave model of motion and field models that allow us to make sense of electric and magnetic phenomena. We need these detailed models because we want to be able to answer questions that the energy-interaction model can’t help us with. But, alas, we will miss the simplicity and generality of the energy model.

# Endnotes

Although we label this model the Three Phase Model of Matter, it is strictly applicable only to pure substances. In addition, there are other phases of matter (such as magnetic phases) that are not discussed as part of this model. Many substances have several different solid phases due to different crystal structures. Some authors define a fourth phase, the plasma phase, in which at least some of the particles are ionized. In this simple model, we ignore these distinctions and focus on only the three primary phases.

In our simple model, we will ignore surface tension and capillarity. The effects of gravity on changes in pressure in a liquid are ignored in this simple model, but will be taken up in Part 2.