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All chemical changes are accompanied by the absorption or release of heat. The intimate connection between matter and energy has been a source of wonder and speculation from the most primitive times; it is no accident that fire was considered one of the four basic elements (along with earth, air, and water) as early as the fifth century BCE. This unit will cover only the very basic aspects of the subject, just enough to get you started; a much more complete set of tutorial lessons can be found here.

Energy is one of the most fundamental and universal concepts of physical science, but one that is remarkably difficult to define in way that is meaningful to most people. This perhaps reflects the fact that energy is not a “thing” that exists by itself, but is rather an attribute of matter (and also of electromagnetic radiation) that can manifest itself in various ways. It can be observed and measured only indirectly through its effects on matter that acquires, loses, or possesses it.

You will recall from earlier science courses that energy can take many forms: mechanical, chemical, electrical, radiation (light), and thermal. You also know that energy is conserved; it can be passed from one "system" to another, but it can never simply disappear.

Kinetic energy and potential energy

In the 17th Century, the great mathematician Gottfried Leibniz (1646-1716) suggested the distinction between vis viva ("live energy") and vis mortua ("dead energy"), which later became known as kinetic energy and potential energy.

Whatever energy may be, there are basically two kinds: kinetic and potential. Kinetic energy is associated with the motion of an object; a body with a mass m and moving at a velocity v  possesses the kinetic energy mv²/2.

Potential energy is energy a body has by virtue of its location in a force field— a gravitational, electrical, or magnetic field. For example, if an object of mass m is raised off the floor to a height h, its potential energy increases by mgh, where g is a proportionality constant known as the acceleration of gravity. Similarly, the potential energy of a particle having an electric charge q depends on its location in an electrostatic field.

A nicely-done elementary tutorial on energy

Thermal energy and chemical energy

All molecules at temperatures above absolue zero are in a continual state of motion, and they therefore possess kinetic energy. But unlike the motion of a massive body such as a baseball or a car that is moving along a uniform trajectory, the motions of individual atoms or molecules are random and chaotic, forever changing in magnitude and direction as they collide with each other or (in the case of a gas,) with the walls of the container.

The sum total of all of this microscopic-scale randomized kinetic energy within a body is given a special name, thermal energy. [Animation link]

Atoms and molecules also possess potential energy in the form of the relative positions of electrons in the elctrostatic fields of their positively-charged nuclei. The potential energies of electrons in the force field created by two or more nuclei can be thought of as "chemical energy", which gives rise to the effects we know as chemical bonding.

Most practical applications of energy involve both kinetic and potential components. For example, a vibrating guitar string exhibits both kinds of energy. It would therefore be more correct to say that chemical energy is mostly potential energy, and thermal energy is mostly kinetic energy.

Molecules are thus both vehicles for storing and transporting energy, and the means of converting it from one form to another when the formation, breaking, or rearrangement of the chemical bonds within them is accompanied by the uptake or release of energy, most commonly in the form of heat.

See the Chem1 Chemical Energetics site for a full treatment of the subject.

 

Energy scales are always arbitrary

You might at first think that a book sitting on the table has zero kinetic energy since it is not moving. In truth, however, that the earth itself is moving; it is spinning on its axis, it is orbiting the sun, and the sun itself is moving away from the other stars in the general expansion of the universe. Since these motions are normally of no interest to us, we are free to adopt an arbitrary scale in which the velocity of the book is measured with respect to the table; on this so-called laboratory coordinate system, the kinetic energy of the book can be considered zero.

We do the same thing with potential energy. If we define the height of the table top as the zero of potential energy, then an object having a mass m suspended at a height h above the table top will have a potential energy of mgh. Now let the object fall; as it accelerates in the earth's gravitational field, its potential energy changes into kinetic energy. An instant before it strikes the table top, this transformation is complete and the kinetic energy ½mv² is identical with the original mgh. As the object comes to rest, its kinetic energy appears as heat (in both the object itself and in the table top) as the kinetic energy becomes randomized as thermal energy.

 

The chemical connection

The same principle applies to chemical substances; we can arbitrarily assign an energy of zero to a mixture of hydrogen and oxygen at 25°C. When they react, a quantity of heat ΔH is given off, and the energy of the resulting H₂O molecules is reduced by that amount. The fact that this energy is negative (with respect to the original H₂ and O₂) simply reflects the particular energy scale we have chosen.

Energy units

Energy is measured in terms of its ability to perform work or to transfer heat. Mechanical work is done when a force f displaces an object by a distance d: w = f × d. The basic unit of energy is the joule. One joule is the amount of work done when a force of 1 newton acts over a distance of 1 m; thus 1 J = 1 N-m. The newton is the amount of force required to accelerate a 1-kg mass by 1 m/sec², so the basic dimensions of the joule are kg m² s^–2.The other two units in wide use. the calorie and the BTU (British thermal unit) are defined in terms of the heating effect on water. For the moment, we will confine our attention to the joule and calorie.

Heat and work are both measured in energy units, but they do not constitute energy itself. As we will explain below, they refer to processes by which energy is transfered to or from something— a block of metal, a motor, or a cup of water.

Heat

When a warmer body is brought into contact with a cooler body, thermal energy flows from the warmer one to the cooler until their two temperatures are identical. The warmer body loses a quantity of thermal energy ΔE, and the cooler body acquires the same amont of energy. We describe this process by saying that "ΔE joules of heat has passed from the warmer body to the cooler one." It is important, however, to understand that

We often refer to a "flow" of heat, recalling the 18th-century notion that heat was an actual substance called “caloric” that could flow like a liquid.

In other words, heat is a process; it is not something that can be contained or stored in a body. It is important that you understand this, because the use of the term in our ordinary conversation ("the heat is terrible today") tends to make us forget this distincion.

 

Work

Work, like energy, can take various forms: mechanical, electrical, gravitational, etc. All have in common the fact that they are the product of two factors, an intensity term and a capacity term. For example, the simplest form of mechanical work arises when an object moves a certain distance against an opposing force. Electrical work is done when a body having a certain charge moves through a potential difference.

type of work	intensity factor	capacity factor	formula
mechanical	force	change in distance	f Δx
gravitational	gravitational potential (a function of height)	mass	mgh
electrical	potential difference	quantity of charge	QΔV

Performance of work involves a transformation of energy; thus when a book drops to the floor, gravitational work is done (a mass moves through a gravitational potential difference), and the potential energy the book had before it was dropped is converted into kinetic energy which is ultimately dispersed as thermal energy.

Mechanical work is the product of the force exerted on a body and the distance it is moved: 1 N-m = 1 J (Illustration from the Ben Wiens Energy site)

Heat and work are best thought of as processes by which energy is exchanged, rather than as energy itself. That is, heat “exists” only when it is flowing, work “exists” only when it is being done.

So you can think of heat and work as just different ways of accomplishing the same thing: the transfer of energy from one place or object to another.

To make sure you understand this, suppose you are given two identical containers of water at 25°C. Into one container you place an electrical immersion heater until the water has absorbed 100 joules of heat. The second container you stir vigorously until 100 J of work has been performed on it. At the end, both samples of water will have been warmed to the same temperature and will contain the same increased quantity of thermal energy. There is no way you can tell which contains "more work" or "more heat".

An important limitation on energy conversion

This limitation is the essence of the Second Law of Thermodynamics which we will get to much later in this course

Thermal energy is very special in one crucial way. All other forms of energy are interconvertible: mechanical energy can be completely converted to electrical energy, and the latter can be completely converted to thermal, as in the water-heating example described above. So although work can be completely converted into thermal energy, complete conversion of thermal energy into work is impossible. A device that partially accomplishes this conversion is known as a heat engine; a steam engine, a jet engine, and the internal combusion engine in a car are well-known examples.

We all have a general idea of what temperaure means, and we commonly associate it with "heat", which, as we noted above, is a widely mis-understood word.

Both relate to what we described above as thermal energy—the randomized kinetic energy associated with the various motions of matter at the atomic and molecular levels.

Heat, you will recall, is not something that is "contained within" a body, but is rather a process in which [thermal] energy enters or leaves a body as the result of a temperature difference. So if we place 10 g of water on a stove until it has absorbed 100 J of heat, for example, then we can say that the water has aquired 100 J of energy.

Temperature

And as we all know, the temperature of the water will rise. Temperature is a measure of the average kinetic energy of the molecules within the water. You can think of temperature as an expression of the "intensity" with which the thermal energy in a body manifests itself in terms of chaotic, microscopic molecular motion.

You will notice that we have sneaked the the word "translational" into this definition of temperature. Translation refers to a change in location: molecules moving around in random directions. This is the major form of thermal energy under ordinary conditions, but molecules can also undergo other kinds of motion, namely rotations and internal vibrations. These latter two forms of thermal energy are not really "chaotic" and do not contribute to the temperature.

Energy is measured in joules, and temperature in degrees. This difference reflects the important distinction between energy and temperature:

• We can say that the 10 g of water we heated on the stove now contains 100 J more energy than it did before. And because energy is an extensive quantity, we know that a 5-g portion of this warmer water contains 50 J more energy than it did originally.
• Temperature, by contrast, is not a measure of quantity; being an intensive property, it is more of a "quality" that describes the "intensity" with which thermal energy manifests itself.

Temperature scales

Although rough means of estimating and comparing temperatures have been around since AD 170, the first mercury thermometer and temperature scale were introduced in Holland in 1714 by Gabriel Daniel Fahrenheit. Fahrenheit established three fixed points on his thermometer. Zero degrees was the temperature of an ice, water, and salt mixture, which was about the coldest temperature that could be reproduced in a laboratory of the time.When he omitted salt from the slurry, he reached his second fixed point when the water-ice combination stabilized at "the thirty-second degree." His third fixed point was "found as the ninety-sixth degree, and the spirit expands to this degree when the thermometer is held in the mouth or under the armpit of a living man in good health.

After Fahrenheit died in 1736, his thermometer was recalibrated using 212 degrees, the temperature at which water boils, as the upper fixed point.Normal human body temperature registered 98.6 rather than 96.

Belize and the U.S.A. are the only countries that still use the Fahrenheit scale.

Temperature is measured by observing its effect on some temperature-dependent variable such as the volume of a liquid or the electrical resistance of a solid. In order to express a temperature numerically, we need to define a scale which is marked off in uniform increments which we call degrees. The nature of this scale— its zero point and the magnitude of a degree, are completely arbitrary.

In 1743, the Swedish astronomer Anders Celsius devised the aptly-named centigrade scale that places exactly 100 degrees between the two reference points defined by the freezing- and boiling points of water.

For reasons best known to Celsius, he assigned 100 degrees to the freezing point of water and 0° to its boiling point, resulting in an inverted scale that nobody liked. After his death a year later, the scale was put the other way around. The revised centigrade scale was quickly adopted everywhere except in the English-speaking world, and became the metric unit of temperature. In 1948 it was officially renamed as the Celsius scale.

Converting between Celsius and Fahrenheit is easy if you bear in mind that between the so-called ice- and steam points of water there are 180 Fahrenheit degrees, but only 100 Celsius degrees, making the F° 100/180 = 5/9 the magnitude of the C° Note the distinction between “°C” (a temperature) and “C°” (a temperature increment). Because the ice point is at 32°F, the two scales are offset by this amount. If you remember this, there is no need to memorize a conversion formula; you can work it out whenever you need it.

 

Absolute temperature scales

Near the end of the 19th Century when the physical significance of temperature began to be understood, the need was felt for a temperature scale whose zero really means zero— that is, the complete absence of thermal motion. This gave rise to the absolute temperature scale whose zero point is –273.15 °C, but which retains the same degree magnitude as the Celsius scale. This eventually got renamed after Lord Kelvin (William Thompson); thus the Celsius degree became the kelvin. It is now common to express an increment such as five C° as “five kelvins”

In 1859 the Scottish engineer and physicist William J. M. Rankine proposed an absolute temperature scale based on the Fahrenheit degree. Absolute zero (0° Ra) corresponds to –459.67°F. The Rankine scale has been used extensively by those same American and English engineers who delight in expressing heat capacities in units of BTUs per pound per F°.

The importance of absolute temperature scales is that absolute temperatures can be entered directly in all the fundamental formulas of physics and chemistry in which temperature is a variable. Perhaps the most common example, known to all beginning students, is the ideal gas equation of state

PV = nRT.

As a body loses or gains heat, its temperature changes in direct proportion to the amount of thermal energy q transferred:

q = C ΔT

The proportionality constant C is known as the heat capacity

C = ΔT / q

If ΔT is expressed in kelvins (degrees) and q in joules, the units of C are J K^–1. In other words, the heat capacity tells us how many joules of energy it takes to change the temperature of a body by 1 C°. The greater the value of C, the the smaller will be the effect of a given energy change on the temperature.

It should be clear that C is an extensive property— that is, it depends on the quantity of matter. Everyone knows that a much larger amount of heat is required to bring about a 10-C° change in the temperature of 1 L of water compared to 10 mL of water. For this reason, it is customary to express C in terms of unit quantity, such as per gram, in which case it becomes the specific heat capacity, commonly referred to as the "specific heat" and has the units J K^–1g^–1.

Note: you are expected to know the units of specific heat. The advantage of doing so is that you need not learn a "formula" for solving specific heat problems.

 

 

 

Specific heat capacities of some common substances

substance C, J /g-K Aluminum 0.900 Copper 0.386 Lead 0.128 Mercury 0.140 Zinc .387 Alcohol (ethanol) 2.4 Water 4.18 Ice (–10° C) 2.05 Gasoline (n-octane) .53 Glass .84 Carbon (graphite/diamond) .710 / .509 Sodium chloride 0.854 Rock (granite) .790 Air 1.01

Note especially the following: The molar heat capacities of the metallic elements are almost identical. This is the basis of the Law of Dulong and Petit, which served as an important tool for estimating the atomic weights of some elements. The intermolecular hydrogen bonding in water and alcohols results in anomalously high heat capacities for these liquids; the same is true for ice, compared to other solids. The values for graphite and diamond are consistent with the principle that solids that are more “ordered” tend to have larger heat capacities.

 

 

Make sure you thoroughly understand the following essential ideas which have been presented above. It is especially imortant that you know the precise meanings of all the highlighted terms in the context of this topic.

• Explain the difference between kinetic energy and potential energy.
• Define chemical energy and thermal energy.
• Define heat and work, and describe an important limitation in their interconversion.
• Describe the physical meaning of temperature.
• Explain the meaning of a temperature scale and describe how a particular scale is defined.
• Convert a temperature expressed in Fahrenheit or Celsius to the other scale.
• Describe the Kelvin temperature scale and its special significance.
• Define heat capacity and specific heat, and explain how they can be measured.

 

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