Values for Backs of Envelopes
- Page ID
- 24451
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)
( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\id}{\mathrm{id}}\)
\( \newcommand{\Span}{\mathrm{span}}\)
\( \newcommand{\kernel}{\mathrm{null}\,}\)
\( \newcommand{\range}{\mathrm{range}\,}\)
\( \newcommand{\RealPart}{\mathrm{Re}}\)
\( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)
\( \newcommand{\Argument}{\mathrm{Arg}}\)
\( \newcommand{\norm}[1]{\| #1 \|}\)
\( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)
\( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)
\( \newcommand{\vectorA}[1]{\vec{#1}} % arrow\)
\( \newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow\)
\( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vectorC}[1]{\textbf{#1}} \)
\( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)
\( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)
\( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)
\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)
\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)| \(\pi\) | pi | 3 |
| G | Newton's constant | \(7 \times 10^{-1} kh^{-1} m^{3} s^{-2}\) |
| c | speed of light | \(3 \times 10^{8} m s^{-1}\) |
| hc | h shortcut | 200 eV nm |
| \(m_{3}c^{2}\) | electron rest energy | 0.5 MeV |
| \(k_{B}\) | Boltzmann's constant | \(10^{-4} eV K^{1}\) |
| \(N_{A}\) | Avogadro's number | \(6 \times 10^{23} mol^{-1}\) |
| R | universal gas constant \(k_{B}N_{A}\) | \(8 J mol^{-1} K^{-1}\) |
| e | electron charge | \(1.6 \times 10^{-19} C\) |
| \(\frac{e^{2}}{4 \pi \epsilon _{0}}\) | electrostatic combination | \(2.3 \times 10^{-28} kg m^{3} s^{-2}\) |
| \(\frac{e^{2}}{4 \pi \epsilon_{0}} /hc\) | fine-structure constant \(\alpha\) | \(0.7 \times 10^{-2}\) |
| \(\sigma\) | Stefan-Boltzmann constant | \(6 \times 10^{-8} W m^{-2} K^{-4}\) |
| \(M_{Sun}\) | solar mass | \(2 \times 10^{30} kg\) |
| \(m_{Earth}\) | Earth's mass | \(6 \times 10^{24} kg\) |
| \(R_{Earth}\) | Earth's radius | \(6 \times 10^{6} m\) |
| AU | Earth-Sun distance | \(1.5 \times 10^{11} m\) |
| \(\Theta _{Moon or Sun}\) | angular diameter of Moon or Sun | \(10^{-2} rad\) |
| day | length of a day | \(10^{5} s\) |
| year | length of a year | \(\pi \times 10^{7} s\) |
| \(t_{0}\) | age of the universe | \(1.4 \times 10^{10} yr\) |
| F | solar constant | \(1.3 kW m^{-2}\) |
| \(p_{0}\) | atmospheric pressure at sea level | \(10^{5} Pa\) |
| \(\rho _{air}\) | air density | \(1 kg m^{-3}\) |
| \(\rho _{rock}\) | rock density | \(2.5 g cm^{-3}\) |
| \(L_{vap}^{water}\) | heat of vaporization of water | \(2 MJ kg^{-1}\) |
| \(\gamma_{water}\) | surface tension of water | \(7 \times 10^{-2} N m^{-1}\) |
| \(P_{basal}\) | human basal metabolic rate | \(100 W\) |
| \(a_{0}\) | Bohr radius | 0.5 Å |
| a | typical interatomic spacing | 3 Å |
| \(E_{bond}\) | typical bond energy | 4 eV |
| \(\varepsilon_{fat}\) | combustion energy density | \(9 kcal g^{-1}\) |
| \(v_{air}\) | kinematic viscosity of air | \(1.5 \times 10^{-5} m^{2} s^{-1}\) |
| \(v_{water}\) | kinematic viscosity of water | \(10^{-6} m^{2} s^{-1}\) |
| \(K_{air}\) |
thermal conduvtivity of air |
\(2 \times 10^{-2} W m^{-1} K^{-1}\) |
| K | ...of nonmetallic solids/liquids | \(2 W m^{-1} K^{-1}\) |
| \(K_{metal}\) | ...of metals | \(2 \times 10^{2} W m^{-1} K^{-1}\) |
| \(c_{p}^{air}\) | specific heat of air | \(1 J g^{-1} K^{-1}\) |
| \(c_{p}\) | ...of solids/liquids | \(25 J mol^{-1} K^{-1}\) |