1.8: Energy
- Page ID
- 357354
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Energy is a ubiquitous term we all use from a young age in a variety of contexts. We sometimes feel like we have no energy or we have a lot of excess energy. Many people now consume “energy drinks.” We think about conserving energy by turning off lights or taking stairs instead of an elevator. Energy is something we encounter daily. We recharge our phones, burn gasoline in cars, feel the heat of the sun, watch as trees sway in the wind, glance up to see if a rock is poised to fall or an icicle is about to drop when we encounter the signs indicating we have entered a zone where that is possible. But what is energy and do the intuitive ideas we develop about energy from an early age align with what we mean by energy from a scientific perspective?
Energy is defined as the ability to do work or as the capacity to cause change. Work has a very specific definition in science, namely that it is a force applied through a distance (w = Fxd). Work is also one of the ways energy can be transferred to and from a system. It is not surprising then that energy and work have the same units – the Joule in the SI system. A joule is the amount of work done when a force of one Newton is applied over a distance of 1 meter. It is also the amount of energy expended during that process.
While the definition may seem circuitous, there are five major ideas associated with the concept of energy that allow us to explain many different phenomena including objects in motion and interactions between particles. One of these ideas is the Law of Conservation of energy which can be simply stated as energy is neither created or destroyed.
Another important idea is that all energy is fundamentally the same, but is manifested in different phenomena in different forms or types. Energy is not directly measured but rather is calculated, and often as a change in energy, based on properties that are measurable such as temperature or speed. Two major types of energy are kinetic energy and potential energy. Kinetic energy is referred to as energy of motion and can be calculated using the formula ½ mv2 where m = mass and v = velocity. Potential energy is referred to as stored energy due to position or composition.
While energy is always conserved, it can be transformed from one type to another. For example, wind, which is really a form of solar energy, turns the blades of a turbine around a rotor connected to a generator, ultimately producing electrical energy that you can use to run your computer or light a room. Energy can be transferred between bodies or systems across boundaries. You may have experienced this holding a cup of a hot drink. Assuming the cup is warmer than your hands, the energy will transfer the cup to your hands - from the hotter region to the colder region. This transfer of energy from regions of different temperature is known as heat. Although related, heat, temperature and thermal energy are not the same. Thermal energy is the energy of the particles in a system due to the random motion of the particles and temperature is a measure of the average kinetic energy of a system.
One final important idea about energy is that you can’t get something for nothing! There is no such thing as a perpetual motion machine. Energy cannot be completely converted to work – some energy is always dissipated as waste heat.