Chemical Energetics: an introduction to chemical thermodynamics and the First Law

# Introduction: the basics of energy, heat and work

On this page:
Energy: what is it?
Energy units
System and surroundings
Observable properties and the state of a system
Heat and work
Concept map

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. In this unit we will review some of the fundamental concepts of energy and heat and the relation between them. We will begin the study of thermodynamics, which treats the energetic aspects of change in general, and we will finally apply this specifically to chemical change. Our purpose will be to provide you with the tools to predict the energy changes associated with chemical processes. This will build the groundwork for a more ambitious goal: to predict the direction and extent of change itself.

One of the interesting things about thermodynamics is that although it deals with matter, it makes no assumptions about the microscopic nature of that matter. Thermodynamics deals with matter in a macroscopic sense; it would be valid even if the atomic theory of matter were wrong. This is an important quality, because it means that reasoning based on thermodynamics is unlikely to require alteration as new facts about atomic structure and atomic interactions come to light.

Energy

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 different ways. It can be observed and measured only indirectly through its effects on matter that acquires, loses, or possesses it.

### 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.

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.

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 increased 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. Electrostatic potential energy plays a major role in chemistry; the potential energies of electrons in the force field created by atomic nuclei play a major role in determining the energies of atoms and molecules.

#### 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 the book is on the table, its potential energy with respect to the surface of the table will be zero. If we adopt this as our zero of potential energy, and then push the book off the table, its potential energy will be negative after it reaches the floor.

### 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. Because of the many forms that energy can take, there are a correspondingly large number of units in which it can be expressed, a few of which are summarized below.

1 calorie will raise the temperature of 1 g of water by 1 C°. The “dietary” calorie is actually 1 kcal. | 1 cal = 4.184 J
1 BTU (British Thermal Unit) will raise the temperature of 1 lb of water by 1F°. | 1 BTU = 1055 J
The erg is the c.g.s. unit of energy and a very small one; the work done when a 1-dyne force acts over a distance of 1 cm. | 1 J = 107 ergs 1 erg = 1 d-cm = 1 g cm2 s–2
The electron-volt is even tinier: 1 e-v is the work required to move a unit electric charge (1 C) through a potential difference of 1 volt. | 1 J = 6.24 × 1018 e-v
The watt is a unit of power, which measures the rate of energy flow in J sec–1. Thus the watt-hour is a unit of energy. An average human consumes energy at a rate of about 100 watts; the brain alone runs at about 5 watts. | 1 J = 2.78 × 10–4 watt-hr 1 w-h = 3.6 kJ
The liter-atmosphere is a variant of force-displacement work associated with volume changes in gases. | 1 L-atm = 101.325 J
The huge quantities of energy consumed by cities and countries are expressed in quads; the therm is a similar but smaller unit. | 1 quad = 1015 Btu = 1.05 × 1018 J
If the object is to obliterate cities or countries with nuclear weapons, the energy unit of choice is the ton of TNT equivalent. | 1 ton of TNT = 4.184 GJ (by definition)
In terms of fossil fuels, we have barrel-of-oil equivalent, cubic-meter-of-natural gas equivalent, and ton-of-coal equivalent. | 1 bboe = 6.1 GJ 1 cmge = 37-39 mJ 1 toce = 29 GJ

System and surroundings

The thermodynamic view of the world requires that we be very precise about our use of certain words. The two most important of these are system and surroundings. A thermodynamic system is that part of the world to which we are directing our attention. Everything that is not a part of the system constitutes the surroundings. The system and surroundings are separated by a boundary. If our system is one mole of a gas in a container, then the boundary is simply the inner wall of the container itself. The boundary need not be a physical barrier; for example, if our system is a factory or a forest, then the boundary can be wherever we wish to define it. We can even focus our attention on the dissolved ions in an aqueous solution of a salt, leaving the water molecules as part of the surroundings. The single property that the boundary must have is that it be clearly defined, so we can unambiguously say whether a given part of the world is in our system or in the surroundings.

> If matter is not able to pass across the boundary, then the system is said to be closed; otherwise, it is open. A closed system may still exchange energy with the surroundings unless the system is an isolated one, in which case neither matter nor energy can pass across the boundary. The tea in a closed Thermos bottle approximates a closed system over a short time interval.

Properties and the state of a system

The properties of a system are those quantities such as the pressure, volume, temperature, and its composition, which are in principle measurable and capable of assuming definite values. There are of course many properties other than those mentioned above; the density and thermal conductivity are two examples. However, the pressure, volume, and temperature have special significance because they determine the values of all the other properties; they are therefore known as state properties because if their values are known then the system is in a definite state.

### Change of state: the meaning of Δ

In dealing with thermodynamics, we must be able to unambiguously define the change in the state of a system when it undergoes some process. This is done by specifying changes in the values of the different state properties using the symbol Δ (delta) as illustrated here for a change in the volume:

ΔV = Vfinal – Vinitial

We can compute similar delta-values for changes in P, V, ni (the number of moles of component i), and the other state properties we will meet later.

Heat and work

Heat and work are both measured in energy units, so they must both represent energy. How do they differ from each other, and from just plain “energy” itself?

First, recall that energy can take many forms: mechanical, chemical, electrical, radiation (light), and thermal, or heat. So heat is a form of energy, but it differs from all the others 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 heat. However, complete conversion of heat into other forms of energy is impossible. This is the essence of the Second Law of Thermodynamics which is covered in another unit; for the moment, we will simply state that this fact places heat in a category of its own and justifies its special treatment.

There is another special property of heat that you already know about: thermal energy can be transferred from one body (i.e., one system) to another. We often refer to this as a "flow" of heat, recalling the 18th-century notion that heat was an actual substance called “caloric” that could flow like a liquid. Moreover, you know that heat can only flow from a system at a higher temperature to one at a lower temperature. This special characteristic is often used to distinguish heat from other modes of transferring energy across the boundaries of a system.

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 heat.

| 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.

When two bodies are placed in thermal contact and energy flows from the warmer body to the cooler one,we call the process “heat”. A transfer of energy to or from a system by any means other than heat is called “work”.

### Interconvertability of heat and work

Work can be completely converted into heat (by friction, for example), but heat can only be partially converted to work. Conversion of heat into work is accomplished by means of a heat engine. The science of thermodynamics developed out of the need to understand the limitations of steam-driven heat engines at the beginning of the Industrial Age. A fundamental law of Nature, the Second Law of Thermodynamics, states that the complete conversion of heat into work is impossible. Something to think about when you purchase fuel for your car!

Concept map

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