ENGG 201 Lecture Notes Sept. 6-19

What is dimensional analysis used for?

to ensure equations are consistent.

What are 4 dimensions used for dimensional analysis?

[M] - Mass
[L] - Length
[T] - Temperature
[t] - time

What are some parameters required for dimensional analysis?

• Terms in an equation need to be dimensionally consistent, i.e. must have the same dimensions
• To determine the dimensions of a term, multiply the dimensions of each parameter in the term.

Conservation Equation

(Input + Generation) = (Output + Accumulation )
"What goes in" + "whatever is created inside" = "Must go out" or "stay inside"

-This equation applies to mass, energy and momentum
- Mass Balance equation is valid for total mass as well as for each chemical species

When is the Generation term important in Conservation Equations?

Generation term is only important when there are chemical reactions

When can the accumulation term be ignored in the Conservation Equation|

when a flowing system is at "Steady-State"

Steps to solve a MB Problem

1. Draw a diagram
a) Identify inlets and outlets
b) Write down all given information from the problem statement
c) Define symbols

2. Write out MB equation for
a) Total
b) Each component

3. Write out mathematical expression for any additional info in the
problem

Composition as a mass% or mole% variables and expression

w = mass fraction
x = mole fraction
m = mass
n = # of moles

numerator = component
denominator = total

mass fraction = m1/mT
mole fraction = n1/nT

*Remember Wm1 + ...Wmc = 1 (or n). Wm1 =/ Xm1.

Conversions between x and w

Energy as a State function

- Energy is a property of the system

Examples: kinetic energy, potential, internal (from molecules moving) energy

Energy as a path function

Energy in transit, how it moves between systems

Examples: Work, heat transfer

What is the driving force for energy transfer in the form of heat?

A difference in temperature

(delta T = Q movement)

Heat capacity:

the energy required to raise the temperature of 1kg of a substance by 1 degree Celsius

What is a system?

the contents in a well-defined space

Define property of a system:

any characteristic of a system

2 types of properties

extensive: size dependent (m, volume)
intensive: size independent (P, T, density, V (specific v))

examples of intensive properties

Specific volume (V)
Molar volume (Vm)
Temperature (T)
Pressure (P)
Density (p = m/v)

examples of extensive properties

Mass (m)
amount of matter (mol),
volume (v)
energy (E)

What is a component

When no reactions are present, every unique chemical substance in a component

- systems can be single (one chemical substance) or multicomponent (more than one)

Two main criteria for a phase.

A phase:
- is homogenous: (same composition throughout)
- has boundaries

Can a gas and vapour phase coexist?

No. A vapour can be condensed into a liquid while a gas cannot.

How many liquid phases can exist for pure substances?

One

How many liquid phases can exist for mixtures?

More than one liquid phase for mixtures of more than one component

How many solid phases can exist?

For pure substances/mixtures, more than one solid phase can exist

Examples of single component, one and two phase systems:

Single: Liquid water
Two: Water vapour and liquid water

Examples of two- component, one and two phase systems:

Single: liquid solution of table salt in water
Two: water and salt solution + solid salt

When does a system attain equilibrium?

when there is no tendency within the system to change its properties (eg. T, P)

Three types of equilibrium in a system:

Thermal Eq'm: Temperature is uniform everywhere in the system
Mechanical Eq'm: Mechanical forces are balanced, pressure is uniform, gravity is negligable
Phase Eq'm: the mass of each component does not change over time

Summary of a system

Equation of the Phase Rule

F = C + 2 - P

C= # of independent components
P = # of phases
F = degrees of freedom

2 types of systems

Non-reactive: # of components = # of unique chemical substances in a system

Reactive: # of components = number of unique chemical species required to make up all of substances in a system

Example of reactive system:

reactive system with H2O, NH3, O2, N2, H2

C = 3 (H, O, N)

If non-reactive, C=5

What is F?

F is the number of intensive variables required to completely fix or specify the system AT EQUILIBRIUM

What happens when F goes to zero?

all of the other intensive variables will have fixed (can't change) values.

What is the Triple Point?

When there are 3 phases, so F = 0 (1 + 2 + 3 = 0), so all values of intensive properties of the phases are fixed by nature

Can there be more than three phases in a one-component system?

No! F would be negative, which is impossible. More than 3 phases cannot exist in equilibrium for a pure substance

What does Equilibrium phase depend on in a single component system?

Temperature and Pressure

Fixing a 1C 1P system

fix T and P, if these are fixed everything else is (like density)

Fixing a 1C 2P system involves:

Specify Temperature OR pressure

3 different combinations of phases

Vapour - Liquid
Vapour - Solid
Liquid - Solid

What happens when you fix PRESSURE in a C1 P2 Liquid-Vapour System?

The Temperature is called the BOILING POINT

When the pressure is 101.325 kPa the temp is called the NORMAL boiling point

What happens when you fix PRESSURE in a C1 P2 Solid-Liquid System?

Temperature is called the FREEZING/MELTING/FUSION POINT

What goes on in a Solid-Vapour C1P2 system?

- happens at a very low pressure

Solid to vapour = sublimination
vapour to solid = DEsublimation

What do the regions/areas of a phase diagram represent?

Single phases

What do the lines in a phase diagram represent?

Two phases (where they coexist)

When three lines converge at a point in a phase diagram, what does that represent?

The Triple Point (all three phases coexist)

What is Tc?

Critical Temperature - the highest temperature at which the substance can exist as a liquid.

What happens when T > Tc

only gas phase exists. If you raise the P, the substance is still a gas

What is the Critical Point?

where the liquid and gaseous phases of a substance merge together into a single phase (gas and liquid coexist). On the Tc line

What is the vapour pressure of a liquid?

The pressure at which a pure liquid can coexist with its vapour at a given temperature (T is Boiling Point)

What is vapour pressure a function of?

Temperature

What is the vapour pressure of a solid?

The pressure at which a pure solid can coexist with its vapour at a given temperature (T is the sublimation point)

What is a process?

a change of conditions (at least one property value changes)

What is an isothermal process?

When T = constant

What is an isobaric process?

When P = constant

What is the dew point?

In an isothermal process, the point where there is mostly vapour and an infinitesimal amount of liquid

What is the bubble point?

In an isothermal process, the point where there is mostly liquid and an infinitesimal amount of vapour

What is specific volume?

V = v/m
V = 1/p (density)
V = m^3 / kg

What is an isotherm?

A constant temperature line

What goes on in a P-V Phase diagram?

C = 1 (because T is constant)
plot Pressure vs specific volume

What is the Lever Rule used for?

to determine relative amounts of phases in 2-phase regions

Lever Rule: 3 important things to note