Working Content> MacroModels > Heat and Temperature
Prerequisites:
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:
- When two objects are placed in close contact, they "share" their hotness or coldness and come to the same degree of warmth.
- 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).
Temperature dimensions and scales
Since we are defining a new arbitrary measurement scale -- temperature -- we might expect that we have to create an independent dimension in addition to our MLTQ set (mass, length, time, and charge). In some older texts this is actually done (and it is called θ -- Greek "theta"). But today, since we know that temperature is a form of energy, we keep Boltzmann's constant, kB = 1.38 x 10-23 J/K, connecting our standard dimension (Joules for mechanical energy) and a temperature measurement (degrees Kelvin).
Three standard temperature scales are in common use in science and everyday life:
- The Celsius scale -- defined to be 0 at the point that ice melts at STP and to be 100 at the point that water boils at STP.
- The Kelvin scale -- one degree Kelvin is defined to have the save size as one degree Celsius, but the 0 is taken to be absolute zero, the temperature at which the matter is in its lowest possible state (quantum ground state).
- The Fahrenheit scale -- defined to be 0 at the lowest possible temperature Fahrenheit was able to get by mixing ice and salts and to be 100 at human body temperature (but it got nailed down before that was reliably measured so normal body temp now averages 98.6o F). It is still used in some scientifically backward countries and relates to Celsius by F = 1.8 C + 32.
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.
Since the chemical reactions that take place in their bodies depend on temperature, animals often care what their temperature is. Some animals adjust their temperature by absorbing heat from their environment. Such animals (for example, lizards) are called ectotherms. They control temperature by moving to where they can absorb more heat, such as into the sun, or where they can absorb less heat, such as into the shade. As a result, their temperature fluctuates considerably through the day and night.
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Photo courtesy E. F. Redish, iguana, Galapagos Islands
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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:
Resources: Mark W. Denny, Air and Water (Princeton U. Press, 1995). ch 8
Joe Redish and Karen Carleton 11/20/11
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