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Our senses provide us with a direct measure of a characteristic of the physical world: whether something feels hot or cold. It took more than a century of hard work by many people (and it's a fascinating story) to figure out what that's all about. The answer is: it's all about motion. Molecules in a gas, a liquid or a solid are always in chaotic, random motion. And it's not just a little bit of wiggling! The random kinetic energy of the molecules in a baseball at rest is 100 times greater than the additional kinetic energy the baseball has when it is thrown as a 100 miles/hour fastball. Ordinary matter has immense hidden energies that we don't notice in our ordinary interactions with the world. Understanding these energies and how to use them occupied much of the 19th century and led to the invention of heat engines and the first industrial revolution.

In developing an understanding of hot and cold we have to refine our experiences and pay attention to three characteristics of this random motion: the total energy of motion contained in an object at rest, the average energy of motion (per molecule or mole), and the flow of this internal random energy from one object to another.

Temperature

The critical new concept is temperature: a measure of the average motion (kinetic energy) of those molecules. There is a temperature, absolute 0 on the Kelvin scale, at which molecular motion stops. However, above this temperature, molecules are always moving. The hotter an object is, the greater the molecular motion. Temperature is critical in our conception of hot and cold because it determines the way the internal random energy will naturally flow -- from hot to cold, that is, from the object with a higher temperature to the object with the lower temperature. If you put a tablespoon of nearly boiling water into a cool lake, energy will flow from the tablespoon of water into the water of the lake, even though there is far more random energy in the lake than in the tablespoon of hot water.

There are many ways to measure temperature. The most common means is to convert a response of some physical object to a change in temperature into a linear scale to characterize how hot or cold an object is.  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), the amount of infrared light given off (in optical thermometers), or the pressure of a dilute gas.

Three distinct concepts

Now let's get more specific. There are three kinds of random motion energy that we need to pay attention to:

1. the total energy, potential and kinetic, of the molecules of an object -- its internal energy (U);
2. the average energy of motion of an individual molecule in an object -- its temperature (T); and
3. internal energy that flows from an object of one temperature to an object in contact with it at a different temperature -- heat (Q) (sometimes heat flow).

The language we use to describe thermal energy is tricky and is used in contradictory ways in different contexts. In physics, especially when we are doing the mathematics of thermal energy, we try to be very careful to distinguish the three. Internal energy is typically represented by U, temperature by T, and heat by Q. These have different mathematical properties. U is extrinsic (proportional to the size of the object), T is intrinsic (density-like: independent of the size of the object); and Q is a given amount of energy -- but it is a transfer of thermal energy. Furthermore, you can't think of U as the "sum of all the Qs" since Q doesn't doesn't play nicely with temperature, each kind of object translating thermal energy into temperature in its own idiosyncratic way.* So in physics, you have to be careful not to confuse these three.

What makes this difficult, is that in chemistry, energy released in an exothermic reaction is also referred to as heat and is often treated as a part of the enthalpy which includes the work needed to make more room for any gases that might be produced. And in biology, where thermal calculations are less common, heat is often used to mean internal energy.  (We admit that even in physics, when we are not in the throes of an actual calculation, we might use that language as well -- but you should try to avoid this until you are confident you can clearly distinguish all three concepts.)

We have said that internal energy, U, is the total amount of energy in an object. This is a tricky concept since there are many kinds of energies that we can identify inside an object: the kinetic energy of the motion of its molecules, the potential energy of their interactions, the kinetic energy of the electrons inside the atoms, and the potential energies of the electron-nucleus interactions (which may be negative if the atoms are bound), and even the mass energy of the atoms through E = mc²! What we pay attention to depends on what transformations we are making. If we are not doing nuclear reactions we can ignore the mass energy. If we are not considering chemical reactions, we can ignore the internal energy of the electrons inside the atoms and molecules. 

All the different kinds of energy hidden inside a chunk of matter can be quite confusing. For this reason, it is a good idea to focus on changes in internal energy, ΔU. Then in any particular example, we can be clear on what part of the internal energy matters in that case.

Although heat is related to temperature, it is not the same thing.  Heat depends on how big the object is and the more mass an object has, the more heat it can contain.  However, temperature is essentially independent of mass or size.  To put more energy into an object, it can be placed in the sun or over a hot flame.  The added heat increases the motion of the molecules and increases the object’s temperature.  Similarly, energy can be removed by placing the object in a snow bank or in a cold mountain stream.  This would slow molecular motion and decrease the object’s temperature.

Biological consequences

Heat and temperature have important biological consequences. Animals often care what their temperature is.  Some adjust their temperature by absorbing heat from their environment. These ectotherms 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.  Other animals generate heat internally.  These endotherms burn fat and sugar to create heat (in the chemical sense) 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).  All endotherms will be homeotherms as the point of generating internal energy is to maintain a constant temperature.

But the most important consequence of our study of heat and temperature is that it will be the start of the science of thermodynamics --  the framework for much more detailed understanding of how energy flows spontaneously, including the first law of thermodynamics (energy conservation) and the second law of thermodynamics (entropy increases / free energy decreases). These provide powerful tools for quantifying the flow of energy in biological systems and describes not only the energy of random motion, our starting point, but how chemical energies interact with other energy systems -- topics of critical importance to understanding biological phenomena!

* Technically, the mathematical point is that "heat" is not a state function, so small bits of transferred thermal energy cannot be integrated to give a unique result. This is one of the reasons for introducing entropy. Small bits of heat divided by the temperature (dQ/T) can be added uniquely and yields the entropy.

Resources: Denny Air and Water ch 8

Follow ons:

• Heat capacity
• Heat transfer
• Biology of heat transfer

Julia Svoboda and Joe Redish 12/24/14