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Expressing quantities properly
1st Semester, 2015/16 Session
Dr. Yeoh Hak Koon
DEPARTMENT OF CHEMICAL ENGINEERING
UNIVERSITY OF MALAYA
(KKEK 1123 Chemical Process Principles 1)
Learning outcomes
At the end of this class, you should be able to
explain basic quantities in chemical engineering
identify dimensions and units
write
quantities and
results of arithmetic operations between quantities
with the appropriate significant figures / digits
D r . Y e o h H a k K o o n 2 0 1 5 2
Part 1: what does it mean? intensive / extensive property? Part 2: what are the dimensions? possible units? Part 3: accuracy, precision? how many significant digits?
Example: The density of a material = ?
Does it depend on how much mass is present?
The dimensions of density =
Possible units are …
Should we write density of water as 103 kg/m3, 996 kg/m3 or what?
D r . Y e o h H a k K o o n 2 0 1 5
The big picture
A quantity has a [value] and [units]
3
Mass Density Concentration Solubility Flow rate Pressure Temperature Energy Enthalpy Gibbs free energy Conversion Extent of reaction Equilibrium constant
You already know most of them Just a new concept:
D r . Y e o h H a k K o o n 2 0 1 5 5
These quantities will haunt you …
Are these
intensive or extensive
quantities?
Intensive or Extensive Quantities
Intensive Quantities
Independent of the amount of materials present, e.g.
temperature
pressure
density, concentration
mass fraction or mole fraction
specific heat capacity, latent heat
Extensive Quantities
Dependent on the amount of materials present, e.g.
mass
weight
moles
volume
energy
heat
D r . Y e o h H a k K o o n 2 0 1 5
Often expressed as ________________
or __________________
6
To compare or describe ‘quality’, e.g.
how salty is the water
which liquid will float
which thing is hotter
which stream is faster
how much energy is needed to melt every kg
we use ______ quantities.
To compare or describe ‘amount’, e.g.
how much material do we have
who is heavier
how much natural gas flows
total energy produced
we use ______ quantities.
D r . Y e o h H a k K o o n 2 0 1 5
Intensive vs. Extensive: when to use which?
7
Depends on our intention:
Fundamental dimensions & units
The most commonly seen in chemical engineering:
Rarer (e.g. in solar power):
D r . Y e o h H a k K o o n 2 0 1 5
Common
symbol
Meaning SI unit cgs unit
(cm, g, s)
American engineering system
M Mass kg g lbm (pound)
N Amount mole mole lbmole (pound mole)
L Length m cm ft (foot, feet)
T Time s s s (second)
Temperature K K oR (degrees Rankine)
Common symbol Meaning SI unit
I Electrical current A
S Luminous intensity cd
10
Derived quantities
Derived quantities = combinations of dimensions to describe more complex items, e.g. volumetric flow rate = volume sent in a given duration (= ) force = mass acceleration (= )
To quantify these derived quantities, we use compound units (i.e. combine units, or define new units), e.g. m3/h kg.m/s2 or N
D r . Y e o h H a k K o o n 2 0 1 5 11
D r . Y e o h H a k K o o n 2 0 1 5
Common derived quantities (chem. eng.)
Quantity Dimensions Common SI units
Molar density / mass density N/L3, M/L3 mole/L, kg/m3
Mass fraction / mole fraction 1 kg/kg, mg/g, mole/mole
Volumetric flow rate L3/T m3/h, L/min
Mass flow rate M/T kg/h, tonne/day
Force ML/T2 N, kN
Pressure M/LT2 kPa, MPa
Energy ML2/T2 kJ, MJ
Power ML2/T3 kW, GW
Specific heat capacity L2/T2 kJ/kg.oC, J/g.K
Latent heat L2/T2 kJ/kg
12
Accuracy: indicates how near each measurement is to the true value Precision: indicates how near repeated measurements are to one another Generally: a number only indicates accuracy
a number standard deviation indicates accuracy + precision
D r . Y e o h H a k K o o n 2 0 1 5 14
Accuracy vs. Precision
Measure the temperature of a liquid with a thermometer (the
smallest scale is 1oC): If T = 41 oC, it means:
Repeat the measurements a few times
Average temperature is _____oC
The standard deviation is roughly 0.48oC, round up to 0.5 oC
Finally report T = ( 0.5) oC
D r . Y e o h H a k K o o n 2 0 1 5 15
Examples
The accuracy of the tool is
half of the smallest scale, or
_____ oC
41.0 40.5 41.5
The true value is in this range.
T (oC)
No. 1 2 3 4
T (oC) 41 42 41 41.5
1. Addition or subtraction: 5.43 MJ + 6 MJ = 11.43 MJ?
The result ranges from
Minimum
Maximum
A difference of
There is an uncertainty of at least ½(1.01) MJ = 0.505 MJ from the average
Report result as
D r . Y e o h H a k K o o n 2 0 1 5 16
Mixing quantities of different accuracy
0.005 MJ
uncertainty
0.5 MJ
uncertainty
11.43
Range of uncertainty
MJ
Dominated by the
larger uncertainty
The 0.03 MJ does not matter as
it is about 10 times smaller than
the expected uncertainty of 0.5 MJ
2. Multiplication or division If = 1.093 g/cm3, & V = 50 cm3, what is V?
The “long-cut”:
Direct multiplication gives 54.65 g
The smallest value of V = ________ g
The largest value of V = ________ g
Uncertainty begins in the _____ digit
So round up the average to _______ g
The “short-cut”:
has ____ significant figures
V has at most ____ sig. fig.
So V _____ g.
D r . Y e o h H a k K o o n 2 0 1 5 17
continued …
Write the answer to the
smallest number of
significant figure
1. Addition / subtraction:
term with the largest magnitude of uncertainty (worst accuracy) decides the final accuracy
2. Multiplication / division: term with the least number of significant figures decides the final number of sig. fig.
To minimize rounding-off errors in manual calculations:
D r . Y e o h H a k K o o n 2 0 1 5
General guide
18
Keep extra significant figures for
intermediate quantities
Part 1: meaning intensive or extensive Part 2: dimensions and units fundamental or derived Part 3: accuracy vs. precision significant figures
Greatest challenge: Part 3 x + y or x – y =?
xy or x/y = ?
D r . Y e o h H a k K o o n 2 0 1 5
Summary
A quantity has a [value] and [units]
19
largest uncertainty decides
smallest sig. fig. decides