What is heat?

You may have heard that there's no such thing as cold. Semantically true. Cold is merely the absence of heat. But what is heat? One thing we know is that when the atoms of one body (an object) are moving more rapidly than those of an identical object, that body is hotter, or contains more heat. Heat is random motion of atoms in a substance. Those atoms may be bound in the molecules of a substance.

Without much of the heat present at room temperature, water exists as the ordered, hydrogen-bonded (see intermolecular forces) crystal ice (left below).

The random thermal motion of each water molecule is insufficient at temperatures below 0ºC to break four H-bond per molecule. As heat is added to ice, the random motion of each water molecule becomes sufficient to break most of the H-bonds (middle panel below). Now H-bonds exist, but they are transient, breaking and reforming frequently. As water absorbs even more heat to become a gas (steam, right panel), each molecule has so much kinetic energy that collisions between molecules increase the spacing between them dramatically.


Heat is random thermal motion, which can occur as translation rotation and vibration of molecules (or just translation for monatomic substances like argon).

A way to think about phases & heat

Imagine that there are 20 of us in a classroom – no desks, and we're holding hands (not necessarily in a big circle, just randomly. The holding of hands will represent hydrogen bonds (or any other intermolecular attractions).

If we stay relatively still, perhaps just shuffling our feet a bit, it will be easy to maintain the hand-holding. That represents the situation in a solid. We just don't have enough translational (moving around) energy to break our bonds.

If we walk around randomly, but calmly, we can probably still hold hands. Sure, once in a while two of us will walk away from each other and lose a grip, but we can quickly reestablish that with someone else. So we have some transient bonds, but all-in-all, we're still mostly holding hands. Such is the situation in liquids.

Finally, imagine if we were all running around flat out, bouncing off of walls and moving again. It would be very difficult to hold hands doing that. Grip strenght just couldn't overcome the our speeds, and on average, very few bonds would exist for very long. Thats the situation in a gas.

Where heat goes in molecules

Heat is motionkinetic energy (KE). It's the motion of atoms, molecules, and atoms within molecules. Now we need to tease apart the relationships between the motion of individual atoms in a molecule and the motions of the molecule as a whole.

First, let's approximate that the relative positions of atoms in a molecule is fixed - all of the bond lengths and angles remain constant (they don't, but we'll make that assumption for now). Now there are two ways a molecule can manifest kinetic energy: translation and rotation


By translation, we mean movement of the whole molecule along any of the three-dimensional coordinates, x, y or z, or any combination thereof. The three Cartesian coordinates form a set of "basis vectors" for translation. Any translation at all can be thought of as a sum of various parts translation along the x, y or z axes. Generally, we identify a unique point in the molecule, the center of mass, and refer to the translation of the center of mass; the rest of it goes along for the ride.


A molecule can also rotate about its center of mass. For most molecules, there are three (never more) independent and perpendicular axes of rotation that are analogous to our three Cartesian axes. For linear molecules, like CO2 (O=C=O) or H2, rotation about the molecules axis carries very little kinetic energy because the nuclei are all on the axis of rotation and electrons are very light. Any rotation at all can be expressed as a sum of various parts of rotation around these three principal axes of rotation.




Now when we relax the constraint on movement of atoms within molecules, we get vibration. In any molecule, bonds between atoms can stretch, compress and bend, and they always do. In any molecule, we can always identify N "normal modes" of vibration (it's N-1 for linear molecules), or "normal vibrations" that are the analogs to translation along the Cartesian axes. Any vibration of a molecule can be expressed as a sum of various parts of its normal modes.

You should check out the section on water to see animations of its three normal modes of vibration.

These three translations, three rotations and N vibrational motions are called degrees of freedom of movement of the molecule, or just degrees of freedom.

Equipartition of Energy

Now we know that any molecule has three "boxes" in which to "store" kinetic energy: translation, rotation and vibration. Notice that a larger molecule (more atoms) obviously has more places to store KE because it has more kinds of vibration or more "vibrational degrees of freedom." Every (nonlinear) molecule has three degrees of translational freedom, three degrees of rotational freedom and N degrees of vibrational freedom, 3N+6 in total (or 3N+5 for a linear molecule).

For most substances over a broad range of temperatures, the law of equipartition of energy holds. It says that energy tends to be distributed evenly over all of the degrees of freedom of a molecule. This has consequences for substances with more and fewer atoms. In the diagram below, each container represents a degree of freedom. The situations for a 3-atom and a 10-atom molecule are illustrated.


Cartesian coordinates

Cartesian coordinates are the normal 2-dimensional (2D) or 3-dimensional (3D) coordinate systems we most-frequently use. In two dimensions, we draw x- and y-axes at 90˚ angles to each other, and in 3D we add a third axis, usually the z-axis, perpendicular to the x-y plane.

The location or direction of an point or particle can be described using Cartesian coordinates (x, y) in the 2D plane, or (x, y, z) in 3D.

The Zeroth Law of Thermodynamics

There are three laws of thermodynamics (1st, 2nd, 3rd) that we will learn in subsequent sections, but often the zeroth law is cited because it lays a good foundation for what comes.

The 0th law says that heat always flows from a hotter object to a cooler one, and never the other way.

This is our general experience with things, though we might need a slight paradigm shift to see it.

When ice is added to a drink, for example, the ice doesn't add cold to the drink, the ice soaks up heat from the warmer liquid, making it cold.

When you touch a cold surface (by which we mean a surface that contains less heat than your hand), heat flows from your hand to the surface. It's always like this: Heat flows from the warmer object to the hotter object until the two are the same temperature, and the heat lost by the hotter object is equal to the heat gained by the cooler object and the surroundings. When you touch a cold object, it feels cold because the heat from your hand is transferring to the cold object.



A paradigm (pair' - a - dime) is a way of seeing something. For example, one way of seeing school is that it is only about accumulating good grades. Another (a paradigm shift for some) is that it is about learning as much as possible about the world.

0th law of thermodynamics

Heat always flows from an object that contains more heat to an object that contains less, and never the other way.

Notation, units and sign convention

We generally use the letter q (or Q) to denote heat; I will generally use the lower case in these web pages.

By long-standing convention, when a system adds heat to its surroundings (loses heat in an exothermic process), the heat is negative (q < 0). When heat is added to a system (endothermic process), the heat is positive (q > 0). Think of this sign convention as being focused on the system; what does the system do?

If it gives off heat, q is negative. If it takes in heat, q is positive.

The SI unit of heat is the Joule (J). 1 J = 1 Kg·m·s-2. Often, in the United States, we still use the calorie. 1 cal = 4.184 J, and 1 cal is the amount of heat required to raise the temperature of 1 cm3 (or 1 ml) of pure water from 0˚C to 1˚C. And remember that we use two kinds of calories, "large C" and "small c." A large-C calorie is one kcal, or 1000 small-c calories.


SI units

SI stands for Système international (of units). In 1960, the SI system of units was published as a guide to the preferred units to use for a variety of quantities. Here are some common SI units


Heat: Sign convention

You can think of a system as being "self-centered." It's all about the world from the point of view of the system

If q > 0, (+q) heat was added to the system in a process (endothermic)

If q < 0, (-q) heat was removed from the system and added to the surroundings by the system (endothermic)

The equivalence of mechanical and heat energy: Joule's experiment

In about 1845, James Prescott Joule (for whom the unit of energy, the Joule, is named), showed that mechanical and heat energy are equivalent. His apparatus is shown here.

He placed a heavy weight (mass = m) on one side, suspended at a height h in the air, giving it a potential energy of E = mgh (g = acceleration of gravity). When the weight falls, the crank turns, moving several paddles around in the central tank of water. By repeating the falling of the weight on either side, Joule was able to show that not only was the water heated by the kinetic energy of the moving paddles, but that the heat added was equal (to within the error of the experiment) to the potential energy released in the falling of the weights.

joule experiment

Source: Hawkins Electrical Guide Number One
(New York: Theo. Audel and Company, 1917) 90

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