Nanomedicine, Volume I: Basic Capabilities

© 1999 Robert A. Freitas Jr. All Rights Reserved.

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

 

APPENDIX A. Useful Data in Medical Nanodevice Design

Compiled from various sources, including (but not limited to) the following References: 10, 460, 536, 537, 567, 763, 1164, 1597, 1662, 2036, 2153, 2154, 2223, 2224, 3229-3232, 3429-3431, 3469.

 

 

I. Systeme International (SI) Metric Prefixes

 

1024 Y- yotta-
1021 Z- zetta-
1018 E- exa-
1015 P- peta-
1012 T- tera-
109 G- giga-
106 M- mega-
103 k-, K- kilo-
102 h- hecto-
101 da-, dk- deka-
10-1 d- deci-
10-2 c- centi-
10-3 m- milli-
10-6 m- micro-
10-9 n- nano-
10-12 p- pico-
10-15 f- femto-
10-18 a- atto-
10-21 z- zepto-
10-24 y- yocto-

 

 

 

II. Units of Measurement and Useful Conversions

 

Angles and Rotations:

180 degrees = p radians  
1 radian = 57.29578 deg = 0.1591549 cycle (revolution)
1 cycle (revolution) = 6.2831853 radians = 360 deg
1 deg = 0.01745329 radian = 0.0027777 cycle
  = 60 arcmin = 3600 arcsec
1 arcsec = 4.848136 microradians  
1 hertz (Hz) = 1 cycle/sec = 6.2831853 radians/sec
1 radian/sec = 9.5492966 revolutions per minute (rpm)  

 

Areas and Surfaces:

1 m2 = 104 cm2 = 106 mm2 = 1012 micron2 = 1018 nm2
  = 1.1959900 yd2 = 10.763910 ft2 = 1550.0031 inch2  
1 acre = 43,560 ft2 = 4046.8564 m2 = 0.0015625 mile2  
1 steradian = 0.079577472 spheres = 3282.8063 deg    
1 sphere = 12.566371 steradians      

 

Concentration:

1 molar (M) = 1 mole/liter = 0.602257 molecules/nm3
1 molecule/nm3 = 1.66042 moles/liter  
1 molal = 1 mole/kg  
milliequivalent:    
  mEq/liter = (mg/liter) x valence / molecular weight
  mEq/kg = (mg/kg) x valence / molecular weight

 

Density:

1 gm/cm3 = 1000 kg/m3 = 8.3454044 lbs/gallon (U.S. liq.)  
  = 1 gm/ml = 1000 gm/liter = 62.42621 lbs/ft3
1 gallon water at 4 oC (U.S. liq.) = 8.34517 lbs = 3.785305 kg  

 

Electrical:

1 coulomb (C) = 1 ampere-sec = 6.24196 x 1018 electron charges
1 ampere (A) = 1 coulomb/sec  
1 volt (V) (electric potential, emf) = 1 joule/coulomb  
  = 1 watt/ampere  
1 ohm (W) = 1 volt/ampere  
1 siemen (S) (conductance) = 1 ampere/volt = 1 mho
1 farad (F) (capacitance) = 1 coulomb/volt  

 

Energy:

1 joule (J) (work, heat) = 1 N-m = 1 W-sec = 1 kg-m2/sec2  
  = 0.000239006 Kcal      
  = 107 ergs = 0.000948451 Btu    
  = 2.7777 x 10-7 kilowatt-hours      
  = 0.00986895 liter-atm      
  = 6.241506 x 1018 eV      
1 nanojoule (nJ) (pJ) = 1000 picojoules = 10-9 joules    
1 zeptojoule (zJ) = 10-21 J = 6.241506 x 10-3 eV    
  = 0.1439325 Kcal      
1 electron-volt (eV) = 160.217733 zJ      
1 MeV = 106 eV = 1000 KeV = 0.001 GeV = 10-6 TeV
1 kilocalorie (Kcal) (= dietary Calories) = 1000 calories = 4184 J  
1 kT at 310 K = 4.28004 zJ = 0.026714 eV    
1 Hartree = 627.5095 Kcal/mole = 27.2116 eV = 4359.7482 zJ  
1 foot-pound = 1.355818 J      
1 megaton (of TNT explosive) ~ 5 x 1015 J    

 

Energy (molar):

1 Kcal/mole = 6.947700141 zJ/molecule  
1 KJ/mole = 29.069177 zJ/molecule  
1 zJ/molecule = 0.1439325 Kcal/mole = 0.0344007 KJ/mole
1 eV/atom = 23.0622 Kcal/mole = 160.217733 zJ/atom

 

Force:

1 newton (N) (force) = 1 kg-m/sec2  
  = 105 dynes = 0.22480894 pounds
1 nanonewton (nN) = 1000 piconewtons (pN) = 10-9 newtons

 

Illumination:

1 candela (cd) (luminous intensity) = 1 lumen/m2
1 lumen (luminous flux) (at 550 nm wavelength) = 0.0014705882 watt
1 candle = 1 lumen/steradian
1 candle/m2 (at 550 nm wavelength) = 0.00462 watt/m2

 

Length and Distance:

1 Angstrom (Å) = 0.1 nm = 10-10 meters  
1 nanometer (nm) = 1000 picometers = 10-9 meters  
1 micron = 1000 nm = 0.001 mm = 10-6 m
1 mile = 5280 ft = 63,360 inches = 1609.344 m
1 light-year = 9.46055 x 1015 m    

 

Magnetism:

1 weber (Wb) (magnetic flux) = 1 volt-sec
1 henry (H) (inductance) = 1 weber/ampere
1 tesla (T) (magnetic flux density) = 1 weber/m2
  = 1 N/ampere-m

 

Mass:

1 kilogram (kg) = 1000 grams (gm) = 2.2046226 pounds (lbs)
  = 771.61792 scruples (apoth) = 15,432.358 grains
1 nanogram (ng) = 1000 picograms (pg) = 10-9 grams
1 pound = 16 ounces (avdp oz) = 453.59237 gm
1 troy ounce = 31.103486 gm = 1.0971429 (avdp) oz
1 gram (gm) = 0.25720597 drams (apoth/troy) = 0.56438339 drams (avdp)
  = 15.432358 grains = 0.77161792 scruples (apoth)
1 ton (metric) = 1000 kg  
1 ton (long) = 2240 lbs = 1016.0469 kg
1 ton (short) = 2000 lbs = 907.18474 kg

1 carat (metric)

= 0.200 grams = 3.08647 grains
1 dalton = 1 amu = 931.752 MeV (mass energy)
  = 1.661 x 10-27 kg/molecule = 1 gm/mole

 

Power:

1 watt (W) = 1 joule/sec = 0.00134102 horsepower = 107 erg/sec
  = 3.41443 Btu/hour = 20.650 Kcal/day  
1 nanowatt (nW) ) = 1000 picowatts (pW = 10-9 watts  
1 horsepower (hp) = 746 W    
2000 Kcal/day = 96.85 W    

 

Pressure or Stress:

1 Pascal (Pa) = 1 N/m2    
1 dyne/cm2 = 0.1 N/m2 (Pa) = 10-6 bars = 0.986923 x 10-6 atm
1 atm = 101,325 N/m2 (Pa) = 1.01325 bars  
  = 760 mmHg = 760 torr = 14.6960 lbs/inch2 (PSI)
1 mmHg = 0.00131579 atm = 133.32 N/m2 (Pa) = 0.00133322 bar
  = 0.0193368 lbs/inch2 = 1.35953 cmH2O  
1 kg/mm2 = 96.784 atm = 9.80665 x 106 N/m2 (Pa)  
  = 1422.33 lbs/inch2 = 98.0665 bars  
  = 106 kg/m2 = 100 kg/cm2  

 

Radioactivity:

1 curie (Ci) = 3.70 x 1010 nuclear disintegrations/sec  
1 bequerel (Bq) = 1 nuclear disintegration/sec = 3.70 x 1010 curies

 

Temperature:

Kelvin (K) degrees = Celsius (C) degrees + 273.15  
1 deg K = 1 deg C (Celsius or Centigrade)  
Fahrenheit (F) degrees = 32 + (9 x Celsius degrees / 5)  
Celsius (C) degrees = 5 x (Fahrenheit degrees - 32) / 9  
310 K = 37 oC = 98.6 oF

 

Time:

1 second = (1 / 31,556,925.9747) of a tropical year    
1 day = 24 hours = 1440 minutes = 86,400 sec
1 year (tropical) = 365.24219 mean solar days ~ p x 107 sec  

 

Velocity:

1 m/sec = 3.2808399 ft/sec = 3.6 km/hr = 2.2369363 mph
  = 1.94385 knots (nautical miles per hour)    
1 mph = 1.609344 km/hr    

 

Viscosity (absolute or dynamic):

1 Poise = 0.1 kg/m-sec = 100 centipoise (cp) = 0.1 Pascal-sec

 

Volume:

1 cm3 (cc) = 1 milliliter (ml)      
1 m3 = 103 liters = 106 cm3 = 1018 micron3 = 1027 nm3
1 cm3 = 1012 micron3 = 1021 nm3 = 10-6 m3 = 10-3 liters
1 micron3 = 109 nm3 = 10-18 m3 = 10-15 liters = 10-12 cm3
1 nm3 = 10-27 m3 = 10-24 liters = 10-21 cm3 = 10-9 micron3
1 liter = 0.001 m3 = 1000 cm3 = 1015 micron3 = 1024 nm3
1 dram (U.S. fluid) = 3.696588 cm3 = 1.040843 drachms (Brit.)    
  = 60 minims = 0.125 U.S. fluid ounces    
1 teaspoon ~ 60 drops ~ 5 cm3    
1 cup = 1 glass = 8 fl. oz. = 16 tablespoons = 48 teaspoons
1 ft3 = 1728 inch3 = 28,316.847 cm3 = 0.037037037 yd3  

1 gallon (U.S. liq.)

= 3785.4118 cm3 = 0.133680555 ft3    
  = 4 quarts = 8 pints = 16 cups = 128 fl. oz. (U.S.)
1 barrel (U.S. petroleum) = 158.9873 liters      
1 acre-foot = 1233.4818 m3      

 

 

 

III. Mathematical and Physical Constants

 

Absolute viscosity:

Water, 310 K: 0.6915 x 10-3 kg/m-sec
Blood plasma, 310 K: 1.1 x 10-3 kg/m-sec

 

Acceleration of gravity:

g = 9.780 39 m/sec2 (sea level at equator)
g = 9.806 21 m/sec2 (sea level at 45o latitude)
g = 9.832 17 m/sec2 (sea level at 90o latitude)

 

Acoustic impedance:

Water: 1.5 x 106 kg/m2-sec
Nylon: 2.9 x 106 kg/m2-sec
Diamond: 6.3 x 107 kg/m2-sec

 

Albedo:

Earth, mean: 31%

 

Angular momentum:

proton (quantized spin): 5.28 x 10-35 J-sec

 

Areal number density:

C atoms, monoatomic graphite sheet: ~38.2 carbons/nm2

 

Atmosphere, Earth:

N2 78.084% (by volume)
O2 20.946%
H2O 0.01% (arctic) - 3% (tropical)
Ar 0.934%
CO2 0.031%

 

Atom and ion diameters (approx.):

H 0.060 nm
F 0.128 nm

O

0.132 nm
N 0.140 nm
C 0.154 nm
He 0.186 nm
Na+ 0.190 nm
S 0.208 nm
P 0.220 nm
Ne 0.224 nm
F- 0.272 nm
O-- 0.280 nm
S-- 0.368 nm
Na 0.372 nm
K 0.462 nm
Fr 0.544 nm

 

Atomic mass unit (amu):

1.661 x 10-27 kg (1/12th of C12 nuclide mass)

 

Avogadro's number:

NA = 6.02257 x 1023 molecules/mole

 

Bandgap:

Silicon: 1.12 eV
Diamond: 5.47 eV

 

Bohr radius:

5.291 772 49 x 10-11 m

 

Boltzmann's constant:

k = 1.380 658 x 10-23 J/molecule-K
  = 8.625 x 10-5 eV/molecule-K

 

Bond energy (covalent, dissociation):

556 zJ (C-C)

 

Bond length:

C-C in graphite: 0.141 5 nm
C-C in diamond: 0.154 448 nm

 

Breakdown voltage, electrical:

Air: 1-3 x 106 volts/m
Porcelain: 4 x 106 volts/m
Titanium dioxide: 3.9-8.3 x 106 volts/m
Paraffin, 25 oC: 9.8 x 106 volts/m
Pyrex glass: 1.3 x 107 volts/m
Paper: 1.4 x 107 volts/m
Nylon, 20 oC: 1.9 x 107 volts/m
Rubber, hard, 25 oC: 1.9 x 107 volts/m
Polystyrene: 2.0-2.8 x 107 volts/m
Teflon: 6 x 107 volts/m
Ruby mica: 1.6 x 108 volts/m
SiC: 4 x 108 volts/m
Diamond: 2 x 109 volts/m

 

Bulk modulus, diamond:

K = (4.4-5.9) x 1011 N/m2

 

Cleavage energy:

Diamond {111} crystal plane: 10.6 J/m2
Diamond {110} crystal plane: 13.0 J/m2
Diamond {100} crystal plane: 18.4 J/m2

 

Compressibility, diamond:

1.7 x 10-11 m2/kg

 

Crack velocity:

Soda-lime glass (maximum): 1580 m/sec
Sapphire (maximum): 4500 m/sec
Diamond (maximum): 7200 m/sec

 

Density:

H2, STP: 0.0899 kg/m3
He, STP: 0.1785 kg/m3
Air, 1 atm, 20 oC: 1.205 kg/m3
Air, STP: 1.2929 kg/m3
N2 at 1000 atm, 37 oC: 493 kg/m3
O2 at 1000 atm, 37 oC: 672 kg/m3
CO2 at 1000 atm, 37 oC: 816 kg/m3
Crude oil: 862 kg/m3 (137 kg/barrel)
Water-ice, STP: 917 kg/m3
Water, 100 oC: 958.384 kg/m3
Water, 37 oC: 993.360 kg/m3
Water, 0 oC: 999.868 kg/m3
Water, 4 oC: 1000.000 kg/m3
Blood plasma, 37 oC: 1025 kg/m3
Glucose: 1562 kg/m3
Silicon, 25 oC: 2330 kg/m3
Boron: 2340 kg/m3
Quartz: 2650 kg/m3
Diamond: 3510 kg/m3
Sapphire: 3970 kg/m3
Germanium, 25 oC: 5323 kg/m3
Earth (mean): 5522 kg/m3
Gadolinium: 7895 kg/m3
Polonium: 9320 kg/m3
Silver, 20 oC: 10,500 kg/m3
Lead, 20 oC: 11,350 kg/m3
Gold, 20 oC: 19,320 kg/m3
Platinum, 20 oC: 21,450 kg/m3

 

Dielectric constant:

Vacuum: 1.00000
Air: 1.00059
Paraffin, 25 oC: 2.0-2.5
Teflon: 2.1
Polystyrene 2.4-2.65

Rubber, hard, 25 oC:

2.8
Nylon, 25 oC: 3.5
Paper: 3.5
Pyrex glass: 4.5
Diamond, 300 K: 5.7
Porcelain: 6.5
Sapphire: 9.0
SiC: 9.0
Ruby, parallel to optical axis: 11.28
Silicon: 12.0
Ruby, normal to optical axis: 13.27
Ethanol, 25 oC: 24.3
Glycerol, 25 oC: 42.5
Water, pure, 37 oC (310 K): 74.31
Water-ice, 0 oC: 88.0
Titanium dioxide: 100.0

 

Distance between adjacent graphite sheets:

0.335 nm

 

e:

2.718 281 828 459

 

Electron mobility:

Diamond (holes): 0.12 m2/volt-sec
Silicon: 0.15 m2/volt-sec
Diamond: 0.18-0.19 m2/volt-sec

 

Electron-volt:

1.602 177 33 x 10-19 J

 

Elementary charge:

1.602 177 33 x 10-19 coulomb

 

Energy content:

Glucose (burned in pure oxygen at 100% efficiency): 4.765 x 10-18 J/molecule
Sugar: ~26 Kcal (~105 J) per "lump"

 

Faraday constant:

96,487.0 coulomb/mole

 

Gravitational constant:

G = 6.67259 x 10-11 N-m2/kg2

 

Gyromagnetic ratio, protons:

4.26 x 107 Hz/tesla

 

Heat capacity (CV):

Air, room temp.: 1.19 x 103 J/m3-K
Water-ice, 77 K: 0.63 x 106 J/m3-K
Water-ice, 249 K: 1.76 x 106 J/m3-K
Diamond: 1.82 x 106 J/m3-K
Water-ice, 271 K: 1.93 x 106 J/m3-K
Platinum, 298 K: 2.84 x 106 J/m3-K
Sapphire: 2.89 x 106 J/m3-K
Water, 310 K: 4.19 x 106 J/m3-K

 

Heat of fusion:

Water, 1 atm, 0 oC: 3.34 x 108 J/m3 (79.7 cal/gm)

 

Heat of vaporization:

Water, 1 atm, 100 oC: 2.17 x 109 J/m3 (539 cal/gm)

 

Hemoglobin:

Atom count, per molecule: ~10,000 atoms/molecule
Free Hb, phagocytic half-life: 10-30 minutes
Molecular weight: ~67,000 daltons
Molecule count, per red cell: ~2.7 x 108 molecules/RBC

 

Lattice spacing at 300 K:

Diamond: 0.356 683 nm
Silicon: 0.543 095 nm
Germanium: 0.564 613 nm
Tin, grey: 0.648 920 nm

 

Magnetic moment:

Electron: 9.2732 x 10-24 J/tesla (Bohr magneton)
Proton: 1.41049 x 10-26 J/tesla

Mass, particle:

Electron rest mass: me = 9.109 389 7 x 10-31 kg
Proton rest mass: mp = 1.672 623 1 x 10-27 kg
Neutron rest mass: mn = 1.674 928 6 x 10-27 kg

 

Mass, planetary:

Atmosphere (Earth): 5.27 x 1018 kg
Oceans (Earth): 1.36 x 1021 kg
Moon: 7.34 x 1022 kg
Earth: 5.98 x 1024 kg
Jupiter: 1.90 x 1027 kg
Sun: 1.97 x 1030 kg

 

Molar volume of ideal gas at STP:

0.022 414 10 m3/mole
37.22 nm3/molecule
0.02687 molecule/nm3

 

Molecular mass:

Diamond: 1.99 x 10-26 kg/atom
Water: 2.99 x 10-26 kg/molecule
N2: 4.65 x 10-26 kg/molecule
O2: 5.32 x 10-26 kg/molecule
CO2: 7.31 x 10-26 kg/molecule
Glucose: 2.99 x 10-25 kg/molecule

 

Molecular number density:

Glucose, solid: 5.24 molecules/nm3
N2 at 1000 atm: 10.6 molecules/nm3
CO2 at 1000 atm: 11.1 molecules/nm3
O2 at 1000 atm: 12.6 molecules/nm3
Water-ice at 273 K: ~30 molecules/nm3
Water, liquid: 33.4 molecules/nm3
Diamond: ~176 carbons/nm3

 

Molecular volume:

Diamond: 0.00567 nm3/atom
Water, liquid: 0.0299 nm3/molecule
O2 at 1000 atm: 0.0791 nm3/molecule
CO2 at 1000 atm: 0.0897 nm3/molecule

N2 at 1000 atm:

0.0943 nm3/molecule

Glucose, solid:

0.1910 nm3/molecule

 

Permeability (magnetic) constant:

m0

= 1.256 637 061 4 x 10-6 henry/m

 

Permittivity (electric) constant:

e0 = 8.854 187 817 x 10-12 farad/m

 

p:

3.141 592 653 589

 

Planck's constant:

h = 6.626 075 5 x 10-34 J-sec  
h = h / 2p = 1.054 572 7 x 10-34 J-sec

 

Power dissipation, global:

Human physiological worldwide: 5.3 x 1011 W (in 1998)
Human technological worldwide: 1.2 x 1013 W (in 1998)
Earth vegetation worldwide: 1.4 x 1014 W

 

Radius, particle:

Proton (Compton wavelength): 1.3214 x 10-15 m
Electron (classical): 2.81777 x 10-15 m

 

Radius, mean planetary:

Moon: 1.738 x 106 m

Earth:

6.371 x 106 m
Jupiter: 6.988 x 107 m
Sun: 6.938 x 108 m
Earth-Moon orbit: 3.80 x 108 m
Earth-Sun orbit: 1.496 x 1011 m

 

Refractive index at l = 589.29 nm (Na):

Air, STP, rel. to vacuum: 1.0002926
Ice: 1.3104
Water, pure, 37 oC: 1.33093
Water, pure, 20 oC: 1.33299
Ethanol, 99.8%, 37 oC: 1.35348
Sucrose, 25% aq. solution, 20 oC: 1.3723
Sucrose, 50% aq. solution, 20 oC: 1.4200
Quartz, fused, 18 oC: 1.45845
Sucrose, 75% aq. solution, 20 oC: 1.4774
Sucrose, 75% aq. solution, 30 oC: 1.4793
Rock salt: 1.544
Glass: 1.52-1.89
Diamond: 2.41726

 

Resistivity:

Diamond, synthesized: 107-108 ohm-m
Diamondoid materials: up to 1010 ohm-m
Diamond, natural, dark: up to 1018 ohm-m

 

Rest mass energy:

(mc2/m) = 8.99 x 1016 J/kg

 

Saturation velocity (electronic):

diamond: 2.7 x 105 m/sec

 

Shear modulus, diamond:

G = (4.8-5.5) x 1011 N/m2

 

Solar constant (at Earth):

1370 W/m2

 

Solar luminosity (mean, total):

3.92 x 1026 W

 

Speed of light in vacuo:

c = 2.99 792 458 x 108 m/sec

 

Speed of sound:

Air, dry, STP: 331.36 m/sec
Water, 15 oC: 1450 m/sec
Water, 37 oC: 1500 m/sec
Sapphire: 10,000 m/sec
Diamond: 17,300 m/sec

 

Standard atmosphere:

1.01325 x 105 N/m2 (760 mmHg)

 

Standard molar gas volume at STP:

22.4141 liter-atm/mole

 

Standard temperature and pressure (STP):

273.15 K and 1 atm

 

Stefan-Boltzmann constant:

s = 5.6697 x 10-8 W/m2-K4

 

Surface area, Earth:

5.10 x 1014 m2

 

Surface energy of graphite:

0.234 J/m2

 

Thermal conductivity (Kt):

Air, 1 atm, 290 K: 0.02524 W/m-K
Glass wool, 293 K: 0.038 W/m-K
Cork, 293 K: 0.042 W/m-K
Wood, 293 K: 0.10 W/m-K
Water, 273 K: 0.561 W/m-K
Water, 310 K: 0.623 W/m-K
Water, 373 K: 0.681 W/m-K
Brick, 293 K: 0.71 W/m-K
Water-ice, 270 K: 1.56 W/m-K
Water-ice, 249 K: 2.21 W/m-K

Sapphire:

  
  normal to c-axis, 310 K: 2-20 W/m-K
  parallel to c-axis, 310 K: 20-40 W/m-K
Lead, 293 K: 35 W/m-K
Platinum, 300 K: 73 W/m-K
Iron, 300 K: 80.3 W/m-K
Aluminum, 300 K: 237 W/m-K
Gold, 300 K: 315 W/m-K
Silver, 300 K: 427 W/m-K
Diamond, natural, 293 K: 2000 W/m-K
Diamond, pure C12, 293 K: 3500 W/m-K
Diamond, natural, 65 K: 17,500 W/m-K

 

Thermal emissivity (er):

Silver, polished: 0.02
Aluminum: 0.022-0.08
Platinum: 0.037-0.05
Porcelain: 0.25-0.50
Brass: 0.60
Water: 0.67
Earth's surface, mean: 0.69
Glass: 0.76-0.94
Cotton cloth: 0.77
Wood: 0.80-0.90
Corundum, emory, 80 oC: 0.86
Snow: 0.89
Paper: 0.93
Asphalt pavement: 0.93
Concrete, rough: 0.94
Ice: 0.97
Human skin: 0.97-0.99
Carbon black: 0.97-0.99

 

Thermal expansion coefficient, linear:

Diamond, 293 K: 0.8 x 10-6/K
Glass, pyrex, 273-373 K: 3.6 x 10-6/K
Sapphire, normal to c-axis, 293 K: 4.5 x 10-6/K
Sapphire, parallel to c-axis, 293 K: 5.5 x 10-6/K
Glass, ordinary, 273-373 K: 8.9 x 10-6/K
Platinum, 273-373 K: 9.0 x 10-6/K
Steel, 273-373 K: 12.0 x 10-6/K
Marble, 273-373 K: 11.7 x 10-6/K
Copper, 273-373 K: 14.1 x 10-6/K
Brass, 273-373 K: 19.3 x 10-6/K
Aluminum, 273-373 K: 23.8 x 10-6/K
Lead, 273-373 K: 29 x 10-6/K
Ice, 363-373 K: 51 x 10-6/K
Hard rubber, 273-373 K: 80 x 10-6/K

 

Thermal expansion coefficient, volumetric:

Vitreous silica, 298 K: 1.2 x 10-6/K
Diamond, 298 K: 3.5 x 10-6/K
Silicon, 298 K: 7.5 x 10-6/K
Silicon carbide, 298 K: 11.1 x 10-6/K
Sapphire, 298 K: 15.6 x 10-6/K
Crystalline silica or quartz, 298 K: 36 x 10-6/K

 

Universal gas constant:

Rgas = 8.206 x 10-5 m3-atm/mole-K
  = 8.314 510 J/mole-K
  = 1.99 cal/mole-K

 

Year, tropical, in ephemeris (mean solar) seconds:

3.155 692 6 x 107 sec

 

Young's modulus:

Sapphire: E = 4.0 x 1011 N/m2
Diamond: E = 1.05 x 1012 N/m2

 

 

Last updated on 17 March 2003