QUANTITIES AND UNITS
(SI – Système International)
Peter GLAVIČ, University of Maribor
Literature
Le Système international d'unités, 7e édition, 1998,
Bureau international des poids et mesures (BIPM), Sevrès
Council directive 80/181/EEC + 85/1, 89/617, 99/103/EC
International standard ISO 31, Quantities and units (1992, '98):
31-0
General principles
31-1
Space and time
31-2
Periodic and related phenomena
31-3
Mechanics
31-4
Heat
31-5
Electricity and magnetism
31-6
Light and related electromagnetic radiations
31-7
Acoustics
31-8
Physical chemisty in molecular physics
31-9
Atomic and nuclear physics
31-10
Nuclear reactions and ionizing radiations
31-11
Mathematical signs and symbols
31-12
Characteristic numbers
31-13
Solid state physics
ISO 1000
SI units and their multiples
ISO 2955
SI units with limited character sets (1983)
ISO 10628
Flow diagrams for process plants (1997)
IUPAC, Quantities, Units and Symbols in Physical Chemistry,
Blackwell Science, Oxford, 1993
CODATA (Committee on Data for Science and Technology)
Values of Fundamental Constants 1998,
Revs. Mod. Phys. 72 (2000) 351
National Institute of Standards and Technology, NIST (1995):
Guide for the Use of the International System of Units (SI)
http//www.physics.nist.gov/Pubs/SP300, http//ts.nist.gov/ts
General principles
QUANTITY
Name:
Symbol
mass
m
UNIT
Name
Symbol
kilogram meter
kg
m
length
l
italics, Times New Roman
PHYSICAL QUANTITY
5 kg,
3m
DIMENSION
dim Q = ABC…
velocity: LT1
force:
LMT2
roman (upright), Arial
Numerical value x Unit
A, B, C, … dimensions of base qt.
, , , … dimensional exponents
L dim of length, T dim of time
M dim of mass
EQUATIONS
E = mc2
between quantities:
v = l/t,
between units:
1 Pa = 1 N/m2
between numerical values:
vkm/h = 3,6lm/ts
between physical quantities: 36 km/h = 10 m/s
Some recommendations for printing symbols
QUANTITIES
ab,
a b,
UNITS
N · m,
N m,
m
s
,
a×b
a
b
a b1
a/b
m/s,
a · b,
m · s1, not ms1 ( = millisecond!)
m · s1;
m · kg/(s3 · A),
m · kg · s3 · A1
MULTIPLES AND SUBMULTIPLES
Do not use multiple prefixes:
10 MV/m
is better than 10 kV/mm,
0,13 mol/kg is better than 0,13 mmol/g
SUB/SUPERSCRIPTS
are roman and Ariel if descriptive:
Ek, Vm, vapH, rHm,
fH  fusH, HCl(g), nB
and italic and Times New Roman if representing quantities:
Cp, CV,
qm,
Kc
Do not attach informations to units:
Vmax = 300 V, not V = 300 Vmax (V - potential difference)
fS (HgCl2, cr, 25 oC) = 154,3 J/(K · mol)
FRACTION, PERCENTAGE
Use space between the number and symbol % or C:
xB = 0,0025 = 0,25 %, not xB = 0,25% or xB = 0,25 percent
% represents a number, do not attach information to it:
mass fraction is 10 % or wB = 10 % or wB = 3 g/kg
Do not use:
percentage by weight, or % (m/m) or % (mol/mol)
Write 0,5 L/L (not 0,5 ppm),
1 nm/m (not 1 ppb),
2 ng/kg (not 2 ppt)
Tabulating numerical values of physical quantities or
Labelling the axes of graphs
Use
t/oC,
not t (oC)
or Temperature (oC),
E/(V/m), not E (V/m) or El. field strength (V/m)
Examples:
T/K
p/MPa
ln (p/MPa)
216,55
0,5180
-0,6578
273,15
3,4853
1,2486
304,19
7,3815
1,9990
2,4
ln p /Mpa
1,6
0,8
0
-0,8
200
220
240
260
280
300
320
T/ K
Equivalent forms in place of 103 K/T:
kK/T, 103 (T/K)1
Terms used in names for physical quantities
Coefficient:
quotient of two quantities of different dimensions:
coefficient of heat transfer, q/T, (W/m2 )/K
Factor:
quotient of two quantities of the same dimension:
friction factor,  = F/Fn, 1 (multiplier of dimension one)
Ratio:
quotient of dimension one of two quantities:
Heat capacity ratio,  = Cp/CV, 1
Fraction:
ratio, smaller than one:
mass fraction, wB = mB/AmA, 1
Level:
logarithm of the ratio of a quantity and its
reference quantity: LF = ln(F/F0) = 1, Np
Constant:
quantity with the same value under all circumst.:
gravitational constant, G = 6,672 59 N · m2/kg2
Masic, specific:
quantity divided by mass, X /m = x:
massic enthalpy, h = H/m, J/kg
Volumic, density:
quantity divided by volume, X/V = x, :
volumic energy, w = W/V, J/m3
Lineic, linear … density: quantity divided by lenth, X/l = …, l:
lineic mass, l = m/l, kg/m
Areic, surface … density: quantity divided by area, X/A = …, A:
areic charge,  = Q/A, C/m2
Molar, »chemical«?: quantity divided by amount, X/n = Xm:
molar volume, Vm = V/n, L/mol
Concentration:
quantity divided by total volume, XB/V = YB:
mass concentration, B = mB/V, kg/L;
(amount-of-substance) concentration, cB = nB/V, mo/L
Some quantities and their units
PERIODIC AND RELATED PHENOMENA
Yearly production
qm
t/a, not: t/yr or tpy
MECHANICS
Pressure
mass flow rate
volume flow rate
p
qm
qV
HEAT
heat
heat flow rate
coefficient of heat transfer
thermal transmittance
surface coefficient of h. t.
heat capacity
massic heat capacity
molar heat capacity
Q

K, (k)
U
h, ()
C
c
Cm
Pa, bar
kg/s
m3/s, L/s
J
W
W/(m2  K)
in building technology only
W/(m2  K)
J/K
J/(kg  K)
J/(mol  K)
PHYSICAL CHEMISTRY AND CHEMICAL PHYSICS
relative atomic mass
Ar
1
relative molecular mass
Mr
1
molar mass
M
kg/mol
concentration
cB
mol/L t, not N or M
The system can be arranged in a matrix form,
similar to the periodic system of elements:
Table 1. Ratios, fractions, concentracions, flow rates etc.
Quantity
Ratio
Fraction
Concentration
Mass
(A/B)
Volume
(A/B)
Amount
r(A/B)
Number
R(A/B)
Mass ratio
Volume ratio
Amount ratio
Number ratio
wB
B
xB
XB
Mass fraction
Volume fraction
Amount fraction
Number fraction
B
cB
CB
Volume
concentration
(Amount)
concentration
Number concen.,
molecular conc.
B
Mass
concentration
Table 2. Volumic, massic, molar (chemical?)
X
A, (S)
A/V = a
V

m
m/V = 
E
E/V = w
Volumic area
m2/m3
Volume fraction
1
Volumic mass
kg/m3
Volumic. energy
J/m3
A/m = s
V/m = v
w
E/m = e
Massic,
Specific
Massic area
m2/kg
Massic volume
m3/kg
Mass fraction
1
Massic energy
J/kg
X/n
A/n = Am
V/n = Vm
m/n = M
E/n = Em
Molar,
Chemical?
Molar area
m2/mol
Molar volume
m3/mol
Molar mass
kg/mol
Molar energy
J/mol
X/V
Volumic,
Density
X/m
Other possibilities for X: number N, work W, enthalpy H, charge Q, price C
Table 3. Flow rate, areic flow rate, volumic flow rate
X
X/t
… flow rate
X/(At)
Areic … flow rate,
not flux
X/(Vt)
Volumic
... flow rate
V
V/t = qV (Q)
m
m/t = qm (q)
n
n/t = F?
Q/J
Q/t = 
Volume flow rate
m3/s
Mass flow rate
kg/s
Amount flow rate
mol/s
Heat flow rate
W = J/s
V/(At) = v
m/(At) = G?
n/(At) = J?
/A = q
Areic volume f. r.,
Average velocity
m3/(m2s) = m/s
Areic
mass flow rate
kg/(m2  s)
Areic
amount flow rate
mol/(m2  s)
Areic
heat flow rate
W/m2
V/(Vt) = ?
m/(Vt) = ?
Volumic
volume flow rate
m3/(m3/s) = s1
Volumic
mass flow rate
kg/(m3  s)
n/(Vt) = v
/V = ?
Volumic
amount flow rate
mol/(m3  s)
Volumic
heat flow rate
W/m3
Other possibilities for X: number N, energy E, charge Q
Table 4. Different conversion rates?
/X
X
… conversion rate
mol/s
V
/V = r
m
/m = r'
A
/A = r''
Volumic conversion rate
mol/(m3  s)
Massic conversion rate
mol/(kg  s)
Areic conversion rate
mol/(m2  s)
Names and symbols of quantities in Chemical Engineering have
to be agreed upon and standardized in the future in order to:
 improve understanding with other engineering disciplines
 ease understanding within the ChE/CAPE community
 foster understanding between ChEs of different countries
 speed up and improve teaching of youngsters