2.1: The Units of Energy

Last updated
Save as PDF

Page ID: 56775

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

The SI unit for Energy is the joule, usually abbreviated J. One joule is equal to one kilogram meter squared per second squared:

\(\ 1 \mathrm{~J}=1 \frac{\mathrm{kg} \mathrm{m}^{2}}{\mathrm{~s}^{2}}\)

Anything that is energy can be written as a number of joules. However, this isn’t the only unit for energy. You are probably more familiar with another unit, the kilocalorie. (A kilocalorie is what is reported as mere Calories in food. The name is unfortunate, for there are 1000 calories in one Calorie; you can easily see how this would lead to confusion.) There are 4,184 joules in a kilocalorie; you can use this with the unit factor method (Section 1.3 to convert between the two forms of energy.)

A unit for energy that will be used more often in this course is the electron Volt, abbreviated eV. The conversion rate to joules is:

\(\ 1 \mathrm{eV}=1.6022 \times 10^{-19} \mathrm{~J}\)

The electron volt is a unit of energy well suited to the processes that happen in atoms. For example, it takes 13.6 electron volts to rip the electron off of a Hydrogen atom. This is a far more convenient number to use than 2.18×10⁻¹⁸, the corresponding number of joules. It is important to remember, however, that the electron volt is the same dimensionality as joules, and that you can freely convert back and forth between the two. The eV is not a unit of voltage, nor, despite its name, is it specific to the electron; you can measure the energy of anything in eV. For example, if you consume 2,000 kilocalories worth of nutrition each day, it would be true, if not terribly illuminating, to say that you consume 5×10²⁵ eV worth of food energy every day.