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1.4: Measures of Power and Energy

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    18939
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    This book brings together topics from a range of fields including chemistry, electrical engineering, and thermodynamics. Scientists in each branch of study use symbols to represent specific quantities, and the choice of variables by scientists in one field often contradict the choice by scientists in another field. In this text, different fonts are used to represent different symbols. For example, \(S\) represents entropy, \($\) represents the Seebeck coefficient, and \(\Bbb{S}\) represents action. A list of variables used in this text along with their units can be found in Appendix A. Use the tables in the appendix as tools.

    Power \(P\) and energy \(E\) are fundamental measures. Power absorbed by a system is the derivative of the energy absorbed with respect to time. \[P =\frac{dE}{dt} \nonumber \]

    In SI units, energy is measured in joules and power is measured in watts. While these are the most common measures, many other units are used. Every industry, from the petroleum industry to the food industry to the electrical power industry, seems to have its own favorite units. Tables \(\PageIndex{1}\) and \(\PageIndex{2}\) list energy and power conversion factors. Values in the tables are from references [7] and [8].

    Conversions between joules and some units, including calories, ergs, kilowatt hours, and tons of TNT are exact definitions [7]. The calorie is approximately the energy needed to increase the temperature of one gram of water by a temperature of one degree Celsius, but it is defined to be 4.1868 J [7]. Note that there is both a calorie and food calorie (also called kilocalorie). The food calorie or kilocalorie is typically used when specifying the energy content of foods, and it is a thousand times as large as the (lowercase c) calorie. Other conversions listed in Table \(\PageIndex{1}\), including the conversion for energy in barrels of crude oil, are approximate average values instead of exact definitions [8]. Values in Table \(\PageIndex{1}\) are listed to the significant precision known or to four significant digits. Other inexact values throughout this text are also specified to four significant digits. The unit 1 cm, referred to as wave number, is discussed in Ch. 6. The conversion value listed in Table \(\PageIndex{1}\) for the therm is the US, not European, accepted value [7]. A barrel, used in the measure of crude oil, is 42 US gallons [8].

    1 J \( =6.241508 \cdot 10^{18}\) electron Volt, eV 1 eV \( =1.602176 \cdot 10^{-19}\) J
    1 J \( =10^{7} \) erg 1 erg \( =10^{-7} \) J
    1 J \( =0.7375621 \) foot pound-force 1 foot pound-force \( =1.355818 \) J
    1 J \( =0.23885 \) calories 1 calorie \( =4.1868 \) J
    1 J \( = 9.47817 \cdot 10^{-4} \) British thermal units, Btu

    1 Btu \( =1055.056 \) J

    1 J \( = 2.3885 \cdot 10^{-4} \) kilocalories (food calories) 1 kilocalorie \( =4186.8 \) J

    1 J \( = 9.140 \cdot 10^{-7} \) cubic feet of natural gas

    1 cubic foot of nat. gas \( =1.094 \cdot 10^{6} \) J
    1 J \( = 2.778 \cdot 10^{-7} \) kilowatt hour, kW·h 1 kW·h \( = 3.6 \cdot 10^{6} \) J
    1 J \( = 6.896 \cdot 10^{-9} \) gallons diesel fuel 1 gallon diesel fuel \( =1.450 \cdot 10^{8} \) J
    1 J \( = 9.480434 \cdot 10^{-9} \) therm (US) 1 therm (US) \( =1.054804 \cdot 10^{8} \) J
    1 J \( = 7.867 \cdot 10^{-9} \) gallons motor gasoline 1 gallon motor gasoline \( =1.271 \cdot 10^{8} \) J
    1 J \( = 2.390 \cdot 10^{-10} \) ton of TNT 1 ton of TNT \( =4.184 \cdot 10^{9} \) J
    1 J \( = 1.658 \cdot 10^{-10} \) barrels crude oil 1 barrel crude oil \( =6.032 \cdot 10^{9} \) J
    1 J \( = 4.491 \cdot 10^{-11} \) metric ton of coal 1 metric ton coal \( =2.227 \cdot 10^{10} \) J
    1 J \( = 1.986447 \cdot 10^{-23} \frac{1}{cm} \) 1 \(\frac{1}{cm} =5.03411 \cdot 10^{22} \) J
    Table \(\PageIndex{1}\): Energy unit conversion factors.
    1 W = 1 \(\frac{J}{s}\) 1 \(\frac{J}{s}\) = 1 W
    1 W \( = 1 \cdot 10^7 \frac{erg}{s}\) 1 \(\frac{erg}{s} = 10^{-7}\) W
    1 W \(= 1.34 \cdot 10^{-3}\) horsepower 1 horsepower \( =7.46 \cdot 10^2\) W
    1 W \( = 2.655224 \cdot 10^3\) foot pound-force per h 1 foot pound-force per h \( = 3.766161 \cdot 10^{-4}\) W
    Table \(\PageIndex{2}\): Power unit conversion factors.

    This page titled 1.4: Measures of Power and 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.