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Expressing quantities properly 1 st Semester, 2015/16 Session Dr. Yeoh Hak Koon DEPARTMENT OF CHEMICAL ENGINEERING UNIVERSITY OF MALAYA (KKEK 1123 Chemical Process Principles 1)

02 Expressing Quantities Students

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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

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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?

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The big picture

A quantity has a [value] and [units]

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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:

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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

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Often expressed as ________________

or __________________

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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.

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Intensive vs. Extensive: when to use which?

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Depends on our intention:

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Dimensions Units

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What is the key difference?

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Fundamental dimensions & units

The most commonly seen in chemical engineering:

Rarer (e.g. in solar power):

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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

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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

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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

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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

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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

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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

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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.

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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:

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General guide

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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 = ?

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Summary

A quantity has a [value] and [units]

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largest uncertainty decides

smallest sig. fig. decides