Working content >MacroModels

Our sensory experience of the world responds to a property of matter that we've mostly ignored in our discussion of motion -- heat and temperature. We all have a familiarity with things being hot or cold and we have a rich vocabulary to describe it.  As scientists have figured out what it means for an object to be hot or cold, the explanation has resolved a number of challenges to the Newtonian explanation of motion in a strange and interesting way. Although you probably know most of the results we will develop in this section, you may not have appreciated how strange some of them are!

A big challenge to the Newtonian theory of motion was the loss of mechanical energy due to non-conservative forces. Energy conservation seems like a very appealing idea. Why should some forces seem to destroy mechanical energy and others not? Why can we think of what some forces do as creating a potential energy and others not? 

I'm sure you already know the answer from previous science classes. Friction, viscosity, and drag steal coherent mechanical energy -- energy associated with the motion of all the molecules of an object moving together in the same way -- and move it into incoherent mechanical energy -- energy associated with the motion of the molecules of an object moving randomly in every which way. We call the latter thermal energy and we describe the increase in this energy as a rise in temperature.

But the strange part of the whole business is that we have a well developed intuition that "everything runs down." From our Newtonian perspective we see that this arises because there are always resistive forces that drain mechanical energy. If they are weak enough, we can ignore them for a time, but eventually, we expect, they will always win and motion will stop. But the reason that they stop is:

Mechanical energy is always conserved but the reason that macroscopic mechanical energy appears to "run down" is because it gets transformed into thermal energy -- the random motion of the molecules of matter -- and, while that might be shifted around and transformed to other forms of energy, there is no mechanism that naturally "drains" thermal energy. It NEVER runs down.

So we are going to have to conclude that macro motion runs down because the energy of motion can be hidden in the temperature of objects. Now temperature appears to "run down" too, because hot things get cooler, but cold things warm up too. The real result, we shall find, is that thermal energy tends to get shared evenly -- but it never goes away. (I can even sometimes be transformed back to coherent mechanical energy.) There is a new "total energy" -- coherent mechanical plus thermal; and we can restore a conservation of energy theorem!

As we get to quantify how much thermal energy is in an object, we will discover that this topic is another place where a careful analysis of the physics of what's going on leads us to see that we live on the small fringes of immense energies! Remember that we learned that matter -- which seems relatively inert -- it just sits there -- in fact consists of positive and negative charges which attract and repel each other  with immense forces. Understanding those forces has led to the mastery of electrical energy and immense changes in the lives of human beings. Similarly, we will discover that the well down which our mechanical energy disappeared is a storehouse of huge thermal energies contained in every object. Understanding these energies led to the first industrial revolution (in the 19th century) and immense changes in the lives of human beings.

Measuring temperature

Although we have an internal measure of how hot and cold things are (though, as we shall see, that's not really what our senses measure), if we want to describe the phenomenon of hot and cold quantitatively, we have to find a way to measure how hot or cold something is. As is often the case when we are starting to define a concept quantitatively, we begin by creating an operational definition -- a process by which we assign a number to the phenomenon. Examples of this are measuring a length or a distance by counting how many standard measuring sticks can be laid end-to-end to match the spatial extent we are trying to measure, using the stretch (a length measurement) of a standard spring to define how to measure force, and using the acceleration of an object feeling a standard force compared to that of a standard mass in order to infer the object's mass.

What we did to measure force was we built on our everyday qualitative understanding of what force does and we found an object that responded to a force with a change that we could measure in terms of things we already knew how to measure -- a spring changes its length when pulled by a force from opposite sides, stretching more if more force is applied. With a spring, we can convert a length measurement into a force measurement by adopting a standard (spring).

For hot and cold, we can begin to generate a way to define how hot or cold something is by making two observations:

1. When two objects are placed in close contact, they "share" their hotness or coldness and come to the same degree of warmth.
2. Some objects expand when they get warmer.

Although the first assumption doesn't appear to always be true (try touching the metal and plastic parts of an object made of both) we'll see that it's not only a good starting point, it turns out to be truer than we expect from our sensory experience -- and that our sensory experience can be misleading!

So to measure how hot or cold something is, we might put a liquid like colored alcohol or mercury in a thin transparent glass tube. We could then observe that as the measuring device was put in increasingly warm liquids, it expanded up the tube. We then calibrate our thermometer by defining two temperatures that anyone can create -- such as melting ice and boiling water -- and defining them as our standards: 0 C and 100 C. We can then divide the length difference up into equal parts and get a result for any temperature in between.

While this is a good starting point, it raises some questions. If we start with different liquids -- say colored alcohol and mercury (both commonly used) -- even if we define the same 0 and 100, does that mean that we will get the same result for temperatures in between? Mightn't the alcohol say, go up faster for the first numbers and slower for the later ones than mercury? This just has to be tested. And eventually, we will get a theoretical understanding of temperature as the average kinetic energy of the molecules of a substance and be able to refine our measuring devices.

Today there are many ways to measure temperature. Examples of some temperature responses include expansion of a liquid (either mercury or alcohol), the voltage across a thermocouple made by joining two dissimilar metals (in a digital thermometer), or the amount of infrared light given off (in optical thermometers).

Technical terminology alert

Just like we had in the case of the term "force", when describing thermal properties of matter there are lots of common speech terms that are used loosely and can take on different meanings. When we talk science, we like to have our terms defined precisely -- even if scientists in their speech (and sometimes in writing) will mix common speech uses with scientific ones! The three terms that we will use that often get confused are:

• temperature -- a measure of the average thermal energy of a substance (proportional to kinetic energy per molecule of the substance)
• internal energy -- a measure of the total thermal energy an object has.
• heat -- the transfer of thermal energy from one object to another.

Each of these will be carefully defined throughout our discussions of the topic and we will try to be consistent about their use.

Biological implications of temperature

Although no organism has learned to use thermal energy as a source of metabolism, the chemical reactions that are life are continually responding to exchanges of energy with other molecules -- that is, they respond to temperature. It's why animals have evolved the mechanism of fever (raising their body temperature) to defend against some infections.

Other animals generate thermal energy internally.  These endotherms burn fat and sugar to convert them to thermal energy and so stabilize their body temperatures.  It is possible to be an ectotherm and find an environment with a relatively stable temperature to maintain a constant body temperature.  So while an ectotherm, such as a snake or turtle, can have a wildly varying body temperature as it moves in and out of the sun (making it a poikilotherm, poikilo- means varied or irregular), other ectotherms such as marine fish stay in water of quite stable temperature to keep their temperature nearly constant.  This makes some fish homeotherms (homeo- means same or similar).  Properly functioning endotherms will be homeotherms as the point of generating internal energy is to maintain a constant temperature.

Follow ons:

• Heat capacity
• Heat transfer
• Biology of heat transfer

Resources: Mark W. Denny, Air and Water (Princeton U. Press, 1995). ch 8

Joe Redish and Karen Carleton 11/20/11