Final Equation Sheet
1
Equations
3
SPU 27, Fall 2010
Constants & Useful Equations
Boltzmann constant
Uinteraction =
3
2 kB T
1 Calorie = 1000 calories = 4.18 kJ
How to measure
ν =B×t
E=
F L0
A0 ∆L
Molecular origin
ν =`×c
E=
kB T
`3
J
kB = 1.38 × 10−23 K
Velocity of molecules at
atmospheric pressure
and temperature
c = 1500 m/s
Heat diffusion constant
of water
D = 1.4 × 10−3 cm2 /s
Avogadro’s number
NA = 6.022×1023 mol−1
ρw = 1 g/cm3
Density of water
(−t/τ )
T (t) = (Tinitial − Texternal ) e
or
initial −Texternal
tcook = τ ln TTtarget
−Texternal
+ Texternal
where τ = L2 /(πD)
Atmospheric pressure
1 atm = 101.325 kPa
g = 9.8 m/s2
Acceleration due to gravity
Troom = 293K= 20◦ C= 68◦ F
Room temperature
Uhydrophobicity = N kB T + Uelectrostatics
Usurface = σ × 4πR2
∆P = 2σ
R
Lshell =
√
πDCa t
N (t) = N0 ekt
k = ln(2)/τ (τ is the doubling time)
Mass of a sphere
of radius R, density ρ
Mass of a shell of radius R,
density ρ, and thickness `
Surface area of a sphere
of radius R
Force
4
2
Conversions
Temperature
T(o C) = T(K)-273K = 95 (T(o F)-32o F)
Length
1 inch = 2.54 cm
Volume
1 L = 1000 cm3 = 10−3 m3
Viscosity
1 cSt = 1 mm2 /s
Energy
1 J = 1 kg·m2 /s2
Pressure
1 Pa = 1 N/m2
Force
1 N = 1 kg·m/s2
Mshell = 4πR2 `ρ
Asphere = 4πR2
F = ma
Bond energy
Type of
Interaction
Van der Waals
Hydrogen bonds
Electrostatic
Covalent bonds
Msphere = 43 πR3 ρ
Interaction
Energy
∼2 kJ/mol
∼5 kJ/mol
∼20 kJ/mol
∼330 kJ/mol
(single covalent bond)