# 3.6 Looking Back and Ahead

- Page ID
- 2390

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)At this point we have developed the energy-interaction approach rather completely. There are still some “kinds” of energy we have not encountered, but when we do, we know what to do: treat it as another energy-system. We know how to approach physical systems that involve changes in macroscopic mechanical energies as well as changes in internal energies. We have a systematic way of “dealing with” friction as the transfer of energy to thermal systems.

We have also refined our model of matter to a point where we can understand most of the thermal properties it exhibits. For certain thermal properties, we can make very definite numerical predictions with our model.

With our model of matter and understanding of energy and energy conservation, we now can actually understand many of the fundamental concepts that underlie much of thermal physics, thermochemistry and the properties of gases, liquids, and solids. We have also developed a much more sophisticated understanding of temperature. We have made a solid connection of the macroscopic concept of temperature that we measure with a thermometer to our extended microscopic model of matter.

Up to this point we have tried to avoid getting into the messy details of the interactions of matter. What is remarkable, is how much we have accomplished with this approach. There are, however, many questions that we cannot answer without getting involved in the details. An example is how do we determine the strength of bonds (or spring force constant). It turns out that the spring constants are directly related to the frequency of vibration of the particles themselves. Infrared spectroscopy is one way to determine these frequencies and thus the spring constants. This is an important question that we definitely want to explore. But before we can proceed, we need to go back and spend some time developing the general connection between unbalanced force and change in motion. In Part 2, we will do this, and can then come back to the question of oscillation frequency of our oscillators.

In the meantime, we will use our model of matter and energy interaction approach, along with some new constructs and relationships to explore other interesting physical phenomena using a very powerful approach to understanding interactions of a chemical and biological nature: the thermodynamic model.

_______________________________________________Endnotes_______________________________________________

A little more about the reasons for the complications here, the reasons we use the labels we have chosen for the energy systems in Chapter 1 (“thermal energy system” and “bond energy system”), and the difference between these macroscopic energy systems and the bond and thermal energies defined within a particle model in Chapter 3. *Remember: material in these footnotes is considered beyond what is necessary or even desirable for the first-time student to worry about when initially learning the basic models.*

First point: Thermal energy system and bond energy system apply to the way to divide up *macroscopically* the internal energy (introduced in Chapter 4) in such a way that when considering physical phase changes, each energy *system* corresponds separately and independently to one or the other of the two empirically observed thermal properties of matter; namely, the specific heat and the heats of melting and vaporization. That is, we *assign* the observed change in energy when the temperature changes to an energy system, that we call the “thermal energy system,” and the magnitude of the change in that energy system is given by the change in temperature multiplied by the heat capacity. Likewise, we assign the observed change in energy when there is a phase change to “bond energy system,” and the magnitude of the change in that energy system is given by the change in mass of a particular phase multiplied by the “heat”—the change in enthalpy—of the respective phase change.

Second Point: Changes in the energy systems defined as above are not always exactly the same as the changes in “thermal energy” and changes in “bond energy” defined from a particle perspective *during a particular physical process* for several reasons. However, the differences are seldom greater than 20% or so, even in the worst case, since they arise due to factors that tend to cancel each other out (ignoring the reduction in heat capacity that typically occurs when a liquid evaporates and the work that is done in a constant pressure measurement of the heat of vaporization).

Third Point: It is appropriate, especially in a models approach, to initially ignore the differences in the macroscopically defined constructs thermal and bond *energy* *systems* and the microscopically defined thermal and bond *energies. *It is possible to thoroughly understand these differences and explicitly deal with them using the understandings of the particle models of thermal and bond energies and thermodynamics, which allow the meaning of measurements of heats of vaporization, for example, to be accurately understood in terms of changes in internal energies. It is not possible to understand this in the context of Chapter 1.

Fourth Point: By taking the approach we have, students can make sense of the macroscopic changes in energy that occur and characterize them using the standard thermal properties of matter in a straightforward way, without getting bogged down in details that are not necessary to understand at this level.