Skip to main content
Engineering LibreTexts

1.3: Conservation of Energy

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    Energy conservation is one of the most fundamental ideas in all of science and engineering. Energy can be converted from one form to another. For example, kinetic energy of a moving ball can be converted to heat by friction, or it can be converted to potential energy if the ball rolls up a hill. However, energy cannot be created or destroyed. The idea of energy conservation will be considered an axiom, and it will not be questioned throughout this book. Sometimes people use somewhat loose language when describing energy conversion. For example, one might say that energy is lost to friction when a moving block slides along a table or when electricity flows through a resistor. In both cases, the energy is not lost but is instead converted to heat. Thermoelectric devices and pyroelectric devices can convert a temperature differential back to electricity. Someone might say that energy is generated by a coal power plant. What this phrase means is that chemical energy stored in the coal is converted to electrical energy. When a battery is charged, electrical energy is converted back to chemical energy. This imprecise language will occasionally be used in the text, but in all cases, energy conservation is assumed. While it might seem like an abstract theoretical law, energy conservation is used regularly by circuit designers, mechanical engineers modeling mechanisms, civil engineers designing pipe systems, and other types of engineers.

    Efficiency of an energy conversion device, \(\eta_{eff}\), is defined as the power output of the desired energy type over the power input.

    \[\eta_{eff} =\frac{P_{out}}{P_{in}} \nonumber \]

    Efficiency may be written as a fraction or a percent. For example, if we say that an energy conversion device is 75% efficient, we mean that 75% of the energy is converted from the first form to the second while the remaining energy either remains in the first form or is converted to other undesired forms of energy. Energy conversion devices are rarely 100% efficient, and some commercial energy conversion devices are only a few percent efficient. Multiple related measures of efficiency exist where the input and output powers are chosen slightly differently. To accurately compare efficiency measures of devices, consistent of input and output power must be used.

    This page titled 1.3: Conservation of Energy is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Andrea M. Mitofsky via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.