The units for energy are surprisingly varied, but it is useful to understand the equivalencies between the different units and the reason for their existence. To derive the units for energy, it is necessary to review the equations from which energy is calculated. While it is not important to fully understand these equations, some equivalencies between the various units used for energy will be discussed later in this chapter. It is also useful to understand that there are various unit systems; however, in any one equation, it is necessary that a consistent unit system be used. The easiest and most widely used unit system is Le Système Internationale d'Unités, the SI unit system. Some people have also referred to this system as the metric system.

Table 2.1 shows the basic units for the common parameters in three different unit systems, the SI system, the British or American customary system, and the centimeter-gram-second (CGS) system.

The three basic units in any unit system are mass, distance, and time. In the SI system, the basic units are kilograms (kg), meters (m), and seconds (s). Velocity is the change in distance with time and is represented as meters per second (m/s). Acceleration is the rate of change of velocity and is represented as meters per second squared (m/s²). According to Newton’s second law of motion, force is equal to the mass times the acceleration. In the SI system, force is measured in newtons (N).

$\mathrm{Force}=\mathrm{Mass}\times \mathrm{Acceleration}$

$1\mathrm{newton}\left(\mathrm{N}\right)=1\mathrm{kg}\mathrm{m}/{\mathrm{s}}^2$

Energy is derived from the equation for work (work and heat are forms of energy). Work is equal to force times the distance moved and, in the SI system, is measured in joules (J).

$\mathrm{Energy}=\mathrm{Force}\times \mathrm{Distance}$

$1\mathrm{joule}\left(\mathrm{J}\right)=1\mathrm{newton}\mathrm{meter}\left(\mathrm{Nm}\right)$

Power is the rate of doing work or the rate of energy conversion. In the SI system, it is measured in watts (W).

$\mathrm{Power}=\mathrm{Energy}/\mathrm{time}$

$1\mathrm{watt}=1\mathrm{joule}/\mathrm{second}\left(\mathrm{J}/\mathrm{s}\right)$

When units are written out in full, capital letters are not used. This includes those units that are named after a person such as newtons, joules, and watts. That is the convention. When units named after a person are abbreviated, they are done so with capital letters. For example, newtons are abbreviated as N, joules are abbreviated as J, and watts are abbreviated as W.

When calculating the amount of energy used by a large country or by the whole world in a year, the numbers can be quite large. When you look at the energy required to accelerate a single subatomic particle in a nuclear reaction, the numbers are very small. That is why in the SI system a variety of prefixes are used to denote a unit being multiplied by a power of 10; for example, the prefix kilo means 1000, 10³, or in scientific notation 1E + 3. The prefixes for the powers of 10 are shown in Table 2.2. The large number prefixes are usually abbreviated with a capital letter and the small power prefixes are abbreviated with a small letter; for example, 1E + 15 joules = 10¹⁵ joules = 1 petajoule = 1 PJ. Similarly, 1E − 15 joules = 10^− 15 joules = 1 femtojoule = 1 fJ. In Figure 1.3, you can see the energy reserves for various countries in exajoules (EJ); 1 exajoule = 10¹⁸ joules = 1 EJ. Later in the chapter you will see that 1 BTU is equal to 1055.056 J; 1 EJ is roughly equal to 1 quadrillion BTU, which is sometimes abbreviated as quads. The energy reserves for countries are often given in quads or exajoules, which are roughly equivalent to each other.

When you receive your electricity bill, the units for the energy used are not joules but kilowatt-hours (kWh). Given that a watt is a joule per second and there are 3600 s in an hour and there are 1000 watts in a kilowatt, 1 kWh = 3,600,000 joules. A typical monthly electric bill might show that you have used 500 kWh charged out at about 10c/kWh. If they had shown the energy usage in joules, it would have been 1.8E + 9 joules, or 1.8 gigajoules (GJ). The electric company uses kWh instead of GJ because people understand kilowatt-hours better than they understand gigajoules. As the electricity bill always uses kWh, electricity consumption and generation tends to be reported in various multiples of watt-hours instead of joules or multiples of joules.

A typical large coal-fired or nuclear-powered electric plant can produce about 1 billion joules of electricity per second, or 1 GJ/s, or 1 gigawatt (GW). Sometimes this is shown as 1000 megawatts (MW) but it really is just a different way of saying the same thing. In 1 day, the 1 GW plant can nominally produce 24 GWh of electricity. In 1 year, the same plant operating 24 h/day and 365 days/year can nominally produce 8760 GWh of electricity. You could also write this as 8.76 terawatt-hours (TWh), which is equivalent to 8.76E + 12 × 3600 joules of energy, or 31.536 PJ.

There are various other units for energy that are also used for various historical reasons. The British Thermal Unit (BTU or Btu) is a unit of energy that, as originally defined in Great Britain, is the amount of energy needed to heat one pound of water by one degree Fahrenheit (°F). Its value can vary depending on the temperature so the International Standards Organization (ISO) has recently set the value to be fixed at 1055.056 joules. A more widely used value, based on the International Steam Table (IT) calorie and defined by the Fifth International Conference on the Properties of Steam (London, July 1956), sets the value of the calorie at exactly 4.1868 joules. This makes the BTU equal to 1055.05585 joules; however, the value set by ISO (1 BTU = 1055.056 joules) is not uncommon.

The calorie is a unit of energy of French origin that, as originally defined, was the amount of energy needed to heat 1 g of water by 1 °C. Its value can also vary depending on the temperature. ISO has recently set the value to be 4.184 joules; however, the value based on the IT calorie was defined by the Fifth International Conference on the Properties of Steam (London, July 1956) to be exactly 4.1868 joules. This conversion factor is also called thermal calories, abbreviated as cal_th.

The calorie is most widely used today to specify the energy gained by human beings when food is digested. Interestingly, one calorie is such a small unit of energy that the food industry uses the kilocalorie to determine the quantity of energy in food; however, they call a kilocalorie a Calorie (with a capital C) and use Calories and kilocalories interchangeably. Understandably, this can create some confusion. I once knew an engineer who looked up the latent heat of melting for ice cream and found it to be 350 J/g. He then looked up the nutritional data on ice cream and found that it contained three Calories per gram of ice cream. He converted the 350 J/g to 84 Calories/g and came to the incorrect conclusion that it took more energy for the body to melt the ice cream than it gained from digesting it. He reasoned that he could eat as much ice cream as he wanted without gaining weight. After eating several gallons of ice cream and gaining about 15 pounds, he realized that something was wrong. He then discovered the confusion between Calories (which are really kilocalories) and Calories. While it does take 84 Calories/g to melt the ice cream, the energy gained from digesting the ice cream is 3 kilocalories/g, or 3000 Calories/g. I am sure that others have been similarly confused by this difference.

An electron-volt (eV) is another specialized unit of energy, particularly common in nuclear reactions. It is defined as the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt. Its use in nuclear reactions will be seen later in Chapter 7.

$1\mathrm{eV}=1.602176487\mathrm{E}-19\mathrm{joules}$

The erg is the unit of energy in the CGS unit system. While this unit system is not very commonly used today and was replaced by the SI unit system, you will occasionally see the erg unit used. It is easy to show that one erg is exactly equal to 10^− 7 J, or 100 nanojoules (nJ). These other (non-SI) units do not use the same prefixes as the SI units, but instead use scientific notation or words for powers of 10, shown in Table 2.2; for example, 7 × 10¹⁵ BTU can be written as 7E + 15 BTU or written out as 7 quadrillion BTU, which can be abbreviated as 7 quads.

Table 2.3 shows the conversions between the important energy unit values. The numbers in the table show how many of the units at the top of the column are equal to one of the units on the left-hand side; for example, 1 Calorie = 4.184 joules.

Sometimes when energy values of different sources are compared, people convert the energy from different fuels into tons of oil equivalent or tons of coal equivalent. To do this, they have to define the energy content of one ton of standard oil. The energy content of crude oil varies from oil to oil but, for the purpose of this conversion, the equivalent oil has been defined as 10 Gcal_th/ton, or 41.868 GJ = 1 ton of oil equivalent (toe). Similarly, one ton of coal equivalent (tce) is defined as 7 Gcal_th/ton of coal; therefore, 29.3076 GJ = 1 tce.

The average energy content of various fuels in BTUs is shown in Table 2.4.

Many homes in the United States and throughout the world are heated with natural gas. One cubic foot of natural gas (measured at standard atmospheric conditions) contains, in approximate round numbers, 1000 BTUs or 1 million joules (1 MJ) of energy when burned. When natural gas is bought and sold, it is usually measured in volumes of one thousand cubic feet (1 MCF for short). The M comes from the Latin word mille, which means thousand, so 1 MCF of natural gas contains ~ 1 million BTUs, or 1 billion joules (1 GJ) of energy. In the United States, invoices sent to homeowners by natural gas utilities showed the gas usage in CCF, which stood for one hundred cubic feet. The Latin word for hundred is centum; hence, one hundred cubic feet was abbreviated CCF. It makes more sense to charge the user for the energy content of the gas used rather than the volume. By consensus, the utility companies switched to charging for the BTUs used. They adopted the therm as the basic unit of energy, and this is what is now displayed in customer invoices. As shown in Table 2.4, 1 therm = 100,000 BTUs. One CCF of gas contains about 100,000 BTU. So, the CCF value previously used and the therm unit currently used are approximately the same.