# 10.1: Energy

## What is Energy?

Energy is one of the most fundamental and universal concepts of physical science, but one that is remarkably difficult to define in a 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.

The concept that we call energy was very slow to develop; it took more than a hundred years just to get people to agree on the definitions of many of the terms we use to describe energy and the interconversion between its various forms. But even now, most people have some difficulty in explaining what it is; somehow, the definition we all learned in elementary science ("the capacity to do work") seems less than adequate to convey its meaning.

### Kinetic energy and potential energy

Kinetic energy is associated with the motion of an object, and its direct consequences are part of everyone's daily experience; the faster the ball you catch in your hand, or the heavier it is, the more you feel it.

Potential energy is energy a body has by virtue of its location. But there is more: the body must be subject to a "restoring force" of some kind that tends to move it to a location of lower potential energy. Think of an arrow that is subjected to the force from a stretched bowstring; the more tightly the arrow is pulled back against the string, the more potential energy it has.

More generally, the restoring force comes from what we call a force field— typically a gravitational, electrostatic, or magnetic field. We observe the consequences of gravitational potential energy all the time, such as when we walk, but seldom give it any thought.

## "Chemical energy"

Electrostatic potential energy plays a major role in chemistry; the potential energies of electrons in the force field created by atomic nuclei lie at the heart of the chemical behavior of atoms and molecules. "Chemical energy" usually refers to the energy that is stored in the chemical bonds of molecules. These bonds form when electrons are able to respond to the force fields created by two or more atomic nuclei, so they can be regarded as manifestations of electrostatic potential energy.

### Interconversion of potential and kinetic energy

Transitions between potential and kinetic energy are such an intimate part of our daily lives that we hardly give them a thought. It happens in walking as the body moves up and down. Our bodies utilize the chemical energy in glucose to keep us warm and to move our muscles. In fact, life itself depends on the conversion of chemical energy to other forms.

Energy is conserved: it can neither be created nor destroyed. So when you go uphill, your kinetic energy is transformed into potential energy, which gets changed back into kinetic energy as you coast down the other side. And where did the kinetic energy you expended in peddling uphill come from? By conversion of some of the chemical potential energy in your breakfast cereal.

### Thermal energy

Kinetic energy is associated with motion, but in two different ways. For a macroscopic object such as a book or a ball, or a parcel of flowing water, it is simply given by ½ mv2. However, when an object is dropped onto the floor, or when an exothermic chemical reaction heats surrounding matter, the kinetic energy gets dispersed into the molecular units in the environment. This "microscopic" form of kinetic energy, unlike that of a speeding bullet, is completely random in the kinds of motions it exhibits and in its direction. We refer to this as "thermalized" kinetic energy, or more commonly simply as thermal energy. We observe the effects of this as a rise in the temperature of the surroundings, or a phase change (like melting). The temperature of a body is direct measure of the quantity of thermal energy is contains.

### Energy units

Work based definition of energy (Joule)

This is the SI unit of energy and one Joule is a Newton meter (J = N.m), where a Newton is the SI unit of force. The Newton (named after Isaac Newton) comes from classical mechanics and Newton's second Law of motion, F = ma (mass times acceleration), and acceleration is the change in velocity per unit time, $$a=\frac{\Delta v}{\Delta t}$$ and velocity is the vectorial change in displacement per unit time, $$v=\frac{\Delta x}{\Delta t}$$ , where x is the displacement in a specific direction. So like any derived SI unit, the Joule can be described in terms of the SI base units, $$1J=1kg\frac{m^{2}}{sec^{2}}$$

Heat based definition of energy (Calorie)

Historically, the calorie is the energy required to raise one gram of water one degree celsius (from 14.5oC to 15.5oC), but today the calorie is considered to be a depreciated unit, and according to NIST Special Publication 1038, "The International System of Units (SI)-Conversion Factors of General Use", the definition of the calorie is based on the Joule:

1cal ≡ 4.184 Joules

Note, the above is a defined number and should not be treated as if it has significant digits. Also, the calorie is actually a very small unit of measurement and it should be noted that the nutritional Calorie (written with a capital C) is really a kilocalorie.

## 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? In our daily language, we often say that "this object contains a lot of heat", but this is gibberish in thermodynamics terms, although it is ok to say that the object is "hot", indicating that its temperature is high. The term "heat" has a special meaning in thermodynamics: it is a process in which a body (the contents of a tea kettle, for example) acquires or loses energy as a direct consequence of its having a different temperature than its surroundings. Hence, thermal energy can only flow from a higher temperature to a lower temperature. It is this flow that constitutes "heat". Use of the term "flow" of heat recalls the incorrect 18th-century notion that heat is an actual substance called “caloric” that could flow like a liquid.

## Test Yourself

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