# What exactly is heat?

Is it energy?

Is it energy per unit volume?

Is it energy per unit time i.e power?

What is it?

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My very basic understanding, is that it's either a certain type of infrared (radiation heat), or the vibration of particles (conduction and convection) – Jonathan. Apr 12 '11 at 22:47
@Jonathan: actually radiation, conduction, and convection are all ways that energy is transferred. The vibrational energy of particles is thermal energy, which is a little different (look at e.g. Ted Bunn's answer). – David Z Apr 12 '11 at 22:59
So the photons(?) that are infrared are also vibrating? – Jonathan. Apr 12 '11 at 23:04
Heat is radiated in all wavelengths, not just infrared. We just most commonly experience heat as infrared but a lot of the heat from sunlight is also in the visible spectrum. – Mark Cidade Apr 13 '11 at 1:21
@Ted Bunn Such cruel chat on "infred heat vibrating" and the like was reason for those youngsters among American textbook writers to replace heat by thermal energy? Obviously in vain. :=) – Georg Apr 14 '11 at 9:12

I'll try to give an answer in purely classical thermodynamics.

Summary

Heat is a way of accounting for energy transfer between thermodynamic systems. Whatever energy is not transferred as work is transferred as heat. If you observe a thermodynamic process and calculate that system A lost $Q$ calories of heat, this means that if the environment around system A were replaced with $Q$ grams of water at 14C and the process were repeated, the temperature of that water would rise to 15C.

Energy

Energy is a number associated with the state of a system. It can be calculated if you give the state variables - things like mass, temperature, chemical composition, pressure, and volume. (These state variables are not all independent, so you only need to give some combination of them.)

Sometimes the energy can be accounted very simply. For an ideal gas, the energy is simply proportional to the temperature, number of molecules, and number of dimensions. For a system with interesting chemistry, internal stresses and deformation, gravitational potential, etc. the energy may be more complicated. Essentially, we get to invent the formulas for energy that are most useful to us.

There's a nice overview of energy, summarizing Richard Feynman, here. For a more theoretical point of view on where these energy formulas come free, see Lubos Motl's answer here.

Energy Conservation

As long as we make the right definitions of energy, it turns out that energy is conserved.

Suppose we have an isolated system. If it is not in equilibrium, its state may change. Energy conservation means that at the end of the change, the new state will have the same energy. (For this reason, energy is often treated as a constraint. For example, an isolated system will maximize its entropy subject to the constraint that energy is conserved.)

This leaves the question of what an isolated system is. If we take another system (the environment) and keep it around the isolated system, we find no observable changes in the environment as the state of the isolated system changes. For example, changes in an isolated system cannot change the temperature, pressure, or volume of the environment. Practically, an isolated system should have no physical mechanisms for interacting with the rest of the universe. Matter and radiation cannot leave or enter, and there can be no heat conduction (I'm jumping the gun on that last one, of course, but take "heat conduction" as a rough term for now). A perfectly isolated system is an idealization only.

Next we observe systems A and B interacting. Before the interaction, A has 100 joules of energy. After interacting, A has 90 joules of energy, so it has lost 10 joules. Energy conservation says that if we measure the energy in system B before and after the interaction, we will always find that system B has gained 10 joules of energy. In general, system B will always gain exactly however much system A loses, so the total amount is constant.

There are nuances and caveats to energy conservation. See this question, for example.

Work

Work is defined by

$$\textrm{d}W = P\textrm{d}V$$

$P$ is pressure; $V$ is volume, and it is fairly easy to give operational definitions of both.

Using this equation, we must ensure that $P$ is the pressure the environment exerts on the system. For example, if we took a balloon into outer space, it would begin expanding. However, it would do no work because the pressure on the balloon is zero. However, if the balloon expands on Earth, it does work given by the product of its volume change and the atmospheric pressure.

That example treats the entire balloon as the system. Instead, we might think of only the air inside the balloon as a system. Its environment is the rubber of the balloon. Then, as the balloon expands in outer space, the air inside does work against the pressure from the elastic balloon.

Work and energy, as described so far, are independent ideas. It turns out that in certain circumstances, they are intimately related.

For some systems, we find that the decrease in energy of the system is exactly the same as the work it does. For example, if we took that balloon in space and watched it expand, the air in the balloon would wind up losing energy as it expanded. We'd know because we measure the temperature, pressure, and volume of the air before and after the expansion and calculate the energy change from a formula.

Meanwhile, the air would have done work on the balloon. We can calculate this work by measuring the pressure the balloon exerts on the air and multiplying by the volume change (or integrating if the pressure isn't constant).

Remarkably, we could find that these two numbers, the work and the energy change, always turned out to be exactly the same except for a minus sign. Such a process is called adiabatic.

In reality, adiabatic processes are approximations. They work best with systems that are almost isolated, but have a limited way of interacting with the environment, or else occur too quickly for interactions beside pressure-volume ones to be important.

In our balloon, the expansion might fail to be adiabatic due to radiation or conduction between the balloon and the air. If the balloon were a perfect insulator and perfectly white, we'd expect the process to be adiabatic.

Sound waves propagate essentially adiabatically, not because there are no mechanisms for one little mass of air to interact with nearby ones, but because those mechanisms (diffusion, convection, etc.) are too slow to operate on the time scale of the period of a sound wave (about a thousandth of a second).

This leads us to thinking of work in a new way. In adiabatic processes, work is the exchange of energy from one system to another. Work is still calculated from $P\textrm{d}V$, but once we calculate the work, we know the energy change.

Heat

Real processes are not adiabatic. Some are close, but others are not close at all. For example, if I put a pot of water on the stove and turn on the burner, the water's volume hardly changes at all, so the work done as the water heats is nearly zero, and what work is done by the water is positive, meaning the water should lose energy.

The water actually gains a great deal of energy, though, which we can discover by observing the temperature change and using a formula for energy that involves temperature. Energy got into the pot, but not by work.

This means that work is not a sufficient concept for describing energy transfer. We invent a new, blanket term for energy transfer that is not done by work. That term is "heat".

Heat is simply any energy transferred between two systems by means aside from work. The energy entering the boiling pot is entering by heat. This leads to the thermodynamic equation

$$\textrm{d}E = -\textrm{d}W + \textrm{d}Q$$

$E$ is energy, $W$ work, and $Q$ heat. The minus sign is a convention. It says the if a system does work, it loses energy, but if it receives heat, it gains energy.

Interpreting Heat

I used to be very confused about heat because it felt like something of a deus ex machina to say, "all the leftover energy must be heat". What does it mean to say something has "lost 30 calories through heat"? How can you look at it and tell? Pressure, temperature, volume are all defined in terms of very definite, concrete things, and work is defined in terms of pressure and volume. Heat seems too abstract by comparison.

One way to get a handle on heat, as well as review everything so far, is to look at the experiments of James Joule. Joule put a paddle wheel in a tub of water, connected the wheel to a weight so that the weight would drive the wheel around, and let the weight fall. Here's the Wikipedia picture of the set up:

As the weight fell, it did work on the water; at any given moment, there was some pressure on the paddles, and they were sweeping out a volume proportional to their area and speed. Joule assumed that all the energy transferred to the water was transferred by work.

The weights lost energy as they fell because their gravitational potential energy went down. Assuming energy is conserved, Joule could then find how much energy went into the water. He also measured the temperature of the water. This allowed him to find how the energy of water changes as its temperature changes.

Next suppose Joule starting heating the water with a fire. This time the energy is transferred as heat, but if he raises the temperature of the water over exactly the same range as in the work experiment, then the heat transfer in this trial must be the same as the work done in the previous one. So we now have an idea of what heat does in terms of work. Joule found that it takes 4.2 joules of work to raise the temperature of one gram of water from 14C to 15C. If you have more water than that, it takes more work proportionally. 4.2 joules is called one calorie.

At last we can give a physical interpretation to heat. Think of some generic thermodynamic process. Imagine it happening in a piston so that we can easily track the pressure and volume. We measure the energy change and the work during the process. Then we attribute any missing energy transfer to heat, and say "the system gave up 1000 joules (or 239 calories) of heat". This means that if we took the piston and surrounded it with 239 grams of water at 14C, then did exactly the same process, the water temperature would rise to 15C.

Misconceptions

What I discussed in this post is the first law of thermodynamics - energy conservation. Students frequently get confused about what heat is because they mix up its definition with the role it plays in the second law of thermodynamics, which I didn't discuss here. This section is intended to point out that some commonly-said things about heat are either loose use of language (which is okay as long as everyone understands what's being said), or correct use of heat, but not directly a discussion of what heat is.

Things do not have a certain amount of heat sitting inside them. Imagine a house with a front door and a back door. People can come and go through either door. If you're watching the house, you might say "the house lost 3 back-door people today". Of course, the people in the house are just people. The door only describes how they left. Similarly, energy is just energy. "Work" and "heat" describe what mechanism it used to leave or enter the system. (Note that energy itself is not a thing like people, only a number calculated from the state, so the analogy only stretches so far.)

We frequently say that energy is "lost to heat". For example, if you hit the brakes on your car, all the kinetic energy seems to disappear. We notice that the brake pads, the rubber in the tires, and the road all get a little hotter, and we say "the kinetic energy of the car was turned into heat." This is imprecise. It's a colloquialism for saying, "the kinetic energy of the car was transferred as heat into the brake pads, rubber, and road, where it now exists as thermal energy."

Heat is not the same as temperature. Temperature is what you measure with a thermometer. When heat is transferred into a system, its temperature will increase, but its temperature can also increase because you do work on it.

The relationship between heat and temperature involves a new state variable, entropy, and is described by the second law of thermodynamics. Statements such as "heat flows spontaneously from hot bodies to cold bodies" are describing this second law of thermodynamics, and are really statements about how to use heat along with certain state variables to decide whether or not a given process is spontaneous; they aren't directly statements about what heat is.

Heat is not "low quality energy" because it is not energy. Such statements are, again, discussion of the second law of thermodynamics.

Reference

This post is based on what I remember from the first couple of chapters in Enrico Fermi's Thermodynamics.

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This answer deserves two upvotes. Alas, I am but one voter. – Colin K Apr 14 '11 at 4:45
Okay, second upvote done. :) – Ernie May 17 '11 at 17:52
+1 for the summary,accurate and crisp. – fedvasu Feb 15 '13 at 20:48

Thermodynamics is concerned with the study of equilibrium states of macroscopic matter. Those equilibrium states are defined so that they can be characterized by just some few extensive parameters like internal energy, volume and number of moles.

Now, the point is that we have then some measured degrees of freedom like energy and volume, but we still have tons of unmeasured degrees of freedom, which we don't mind describing in detail when dealing with equilibrium states.

A change on some degree of freedom is then associated with a change in energy. The changes on the measured degrees of freedom gives rise to a form of energy transfer called work. One example is the following: consider some gas with volume $V$, then the mechanical work is the transfer of energy related to a change in the volume (which is a measured degree of freedom). This work is then $-P dV$.

Now, although you can't see in detail the unmeasured degrees of freedom, you can't simply ignore them, because they are there. Thermodynamics reserves one special variable to hold information about those degrees of freedom we don't have access macroscopically, it is the entropy $S$.

The exchange of energy due to changes on those unmeasured degrees of freedom is then isolated from the change of energy due to changes on the measured ones. This form of change of energy is called heat. It can be written as $TdS$.

This description makes it easier to understand then why we have a chemical work $\mu dN$ and another kinds of work. Look that $TdS$ has the same form as those other forms of energy transfer. The real difference is that $S$ is the variable accounting for the unmeasured degrees of freedom and this transfer of energy is that you don't measure directly but just its effects on macroscopic level.

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read about molecular / statistical description of thermal energy (which is not heat) u would really get the feel what it really is.

as far as the rigorous description of heat is in terms of entropy, let me denote it by q and entropy by s (dq is total differential of q)

dq<=Tds

equality being true for reversible process.

you may come across many intuitive(mostly wrong) definitions and descriptions of heat. Some of which may still work if you are a mechanical engineer dealing with simple (linear) thermal/fluid systems but if you are a physicist, you really need to know entropy and heat in terms of it.

dimensionally q (heat) is equal to energy

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Energy can be defined as the capacity to do work or produce heat (among others)

You can define a system through defining its boundaries, then energy flowing across system boundaries could be heat or work.

Although Energy can exist contained in a system as potential ( in many forms) to exchange it from one system to another it takes (or it is named as) these specific forms: heat and work.

What is the difference between heat and work?

Mechanical work is a force acting through a distance in certain direction, it's relevant and useful for our daily tasks, like moving an arm, a piston, a machine, then a car, etc.. it's in a given preferential direction, this energy can be used to respond to some intention over the -whole system-, that's one of the reasons it's often called useful energy.

On the other hand at microscopic scale particles are too many, and not so easy to control, they have no preferential direction of movement, particles vibrates, and move randomly, they do not move in a coherent direction although they have a mean speed (related to system temperature). It's a kind of symmetry in the sense of having no preferential direction, but this kinky energy, can be transfered, so that isotropy, with dissipated amount of "surprises" and information, crosses the boundaries under the name of Heat, turning the interacting systems to a whole boring dead state (to witch systems usually evolve).

Heat flows from High to Low temperature systems. Changes in the systems made through heat are strongly path dependent (its effects depend on pressure, volume, time, temperature differences, order of events ..)

Finally, mechanical work, besides to produce the moving of large ammount of particles in a coherent direction, this "intended action" generate of course at microscopic scale a lot of "unintended actions" too (random), and that's heat again, then work is never alone.

Work can be converted completely into heat, but heat can not be converted completely into work. That's why heat is usually seen as energy loss, and even the definition of energy is often : the ability a physical system has to do work (leaving The Heat out)

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Three meanings:

1. amount of energy (in joules) transfered from a "hot body" to "cold body"

2. the process of 1.

3. a non exact 1-form Q such that $dE=W+Q$ or $Q=TdS$

Heat is not a substance. Heat cannot be "extracted" from a body. Microscopically heat is "the flow of kinetic energy" during the process of achieving thermal equilibrium.

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""Heat cannot be "extracted" from a body"" Of course You can! :=) What does a refridgerator do? – Georg Apr 12 '11 at 18:40
the process of 1? I got into a loop – HDE Apr 12 '11 at 19:36
@Georg, I think he meant, there isn't a "heat particle" which you physically pick up and take out. – Jonathan. Apr 12 '11 at 22:48
Yeah, I meant that heat is a label for the process (and(!) for the amount of energy transfered). Somehow "heat tranfer" is misleading, but one should not be too pedantic. – foobar Apr 13 '11 at 19:18

The word "heat" is used to apply to energy transfer from a high-temperature body to a low-temperature body. You should never say that a body contains a certain amount of heat; you should only say that a certain amount of heat flowed from one body to another. As Nic correctly says, it comes in units of energy (joules, or sometimes calories).

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Of course a body contains heat. The fact that heat is not a substance, does not mean it cannot be "contained". – Georg Apr 12 '11 at 18:41
I doubt that we disagree on the physics, but as a purely semantic matter of English-language usage, your statement is incorrect. Objects contain thermal energy; they transfer heat. I promise. – Ted Bunn Apr 12 '11 at 18:43
A common expression is "heat capacity". Capacity without containing something? – Georg Apr 12 '11 at 20:29
@Georg: for one thing, there's no requirement that the meaning of a composite phrase like "heat capacity" be the same as the meaning of its individual words. Besides, AFAIK this is in the sense of "capacity to absorb heat." (If this is going to turn into an extended discussion it would be good to take it to chat) – David Z Apr 12 '11 at 22:42
@Georg: your literature is obviously dated and/or not English. What Ted says is completely correct. Of course, it doesn't mean that people (even authors of books) can't misuse the expression. You are a living example of that :) – Marek Apr 13 '11 at 6:35

Its largely a historical artifact. But it is often used to refer to energy. In any physics text book it will be meant as analagous to energy and so measured in joules.

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Heat is what it alwas was: a form of energy. Never a historical artifact! How would You deal with, say a Carnot cycle, when You had to say "historic artefact" instead of heat and work and entropy? – Georg Apr 12 '11 at 18:43