process thermodynamics by sandler
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8/14/2019 Process thermodynamics by sandler
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Chapter 1 IntroductoryMaterial
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• Internal Energy: associated withmolecular motion and interactions
• External Energy: associated with thecenter of mass of a system
– For example, the kinetic and potentialenergy of throwing a ball in the air.
• (Thermodynamic) State: the
properties of a system defined byspecific physical or thermodynamicvariables
Thermodynamics Basics: Energy
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• System: a specific volume inspace defined by user.
• Surroundings: the rest of the
universe outside of a system• Boundary: the surfaceseparating the system fromsurroundings either real or
invented• State of Agglomeration (or
Phase): the form of the materialeither solid, liquid, or vapor.
Thermodynamics Basics: Systems
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• Heat: flow of energy due to temperaturedifferences on each side of a boundary
• Work: flow of mechanical motion across aboundary
• Mechanical Contact: a physical boundary
that allows changes in pressure (or work) inthe system to change that in thesurroundings and vice-versa
• Rigid: a boundary that does not deform withpressure
• Thermal Contact: a boundary that allowsheat to cross
• Adiabatic: a system whose boundary doesnot allow heat to cross
Thermodynamics Basics: Contact
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• Open: a system that allowsmass to cross the boundary
• Closed: a system that does
Not allow mass to cross theboundary
• Isolated: a system whoseboundary does not allow anymass, heat, or work to cross
Thermodynamics Basics: Contact
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• Letters: M ≡ mass; N ≡ moles; V ≡ Volume; U≡ Internal Energy; H ≡ Enthalpy; A≡Helmholtz; G ≡ Gibbs; P ≡ Pressure; T ≡Temperature; t ≡ time
• Underbar ≡ Molar Property
– V= total volume [cm3
]; V = molar volume [cm3
/mol](V= V * N)
• “Hat” ≡ Specific (mass) Property – is specific volume [cm3 /g]
• Overbar ≡ Partial molar property
– Partial Molar Volume
– Except ≡ Mixture Fugacity
Nomenclature
V ̂
f
iV
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• Extensive variables depend on size – The Volume, V , of water in a beakerdepends on how much water that you put init.
• Intensive variable: scaled by mass ormoles, – e.g. molar volume V = V/N, as long as T & P
remain constant, V will remain the same witheither 1 ml or 1000 ml of water
– T , and P are exceptions• P [Pa] : 1 Pa = 1 N/m2 = J/m3 = kg / m /s2
• T…. I dunno
Types of Variables: Intensive/Extensive
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• Elements and Compounds usually have at least 3 states of
matter (aka. states of aggregation): Solid, Liquid, Vapor
• “Fluid” is a term for a vapor/gas OR Liquid
• “Supercritical Fluid” is a substance above its critical point
States of Matter
P
Pc
TcT
Supercritical
Fluid
LIQUID
Critical Point
P c
SOLID
VAPOR
Critical Point:
Max T & P in
which
Liquid and
Vapor can
coexist
Triple Point
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• Each phase has a transitionto the other:
– Vaporization (Liquid-to-Vapor
; and vice-versa)
– Melting (Solid-to-Liquid)
– Sublimation (Solid-to-Vapor)
• If you are exactly at the T & P conditions of the
transitions, then you are in 1 component phase
equilibrium (see Chapter 7 & onward) also called “saturation”
– Each Phase Coexists and Each phase has its
own thermodynamic properties, U, H, V, etc.
• In property diagrams, you will see “envelopes” where
each side of the envelopes represents the two phases
States of Matter: Transitions & Equilibrium
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Chapter 2:
Conservation of Mass
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• Balances! • Material Balance:
• Control
Volume
– Surface
through
which
mass
passes
– Multiple
entrances/exits (M can be negative if out)
What did you Learn in CPE211?
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• Choosing the right control volume is sometimes
more of an “art” than science – Actually based on experience
• Sometimes multiple control volumes are correct – Some are easier to implement and use than
others.
• Types: – Static (non-changing) – Volume changes from beginning to end – Constant mass/moles – Closed
– Open – Etc. etc.
• Be Creative
Control Volumes
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• In this Book, any flow (crossingof a control volume boundary)Entering into a system has aPOSITIVE (+) Sign.
• Any Flow Exiting a system has
a NEGATIVE (-) Sign.• Thus, We will not use “in minus out”, but wewill sum all flows and let their signs andmagnitudes determine what the accumulationis.
– In the diagram above, M 1, 2, and k , may be inlets andthus positive signs, while M 3 may be an exit andthus a negative sign.
• You will see this will be consistent with thesigns of heat and work flows in Chap. 3.
Control Volume and Signs
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• There are two Main Types of Balance Equations:
Difference and Differential.• Difference: the change in material determined
from a subtraction of the system contents at twodifferent times or at two different conditions
• Differential: the change of material over time(RATE) from calculus
• The difference equations are nothing more thanthe differential equations integrated over a timeperiod.
• Each Type has two sub-types based on Massunits OR Mole units
– Thus, Difference (mass or mole); & Differential(mass or mole)
Balance Equations
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• For any real system, you will most often be assigning
numbers to represent certain components,inlets/outlets, reactions, phases (CPE512), etc.
• In this course,C = total number of Components in the systemK = total number of Inlets/Outlets
M = total number of Independent Reactions• Variables will have subscripts to identify each of the
parts that combine to make C, K & M – i = the component number, with the number that represents
C as the last in the series and the total number
– k = the inlet or outlet ID number withK
being the lastinlet/outlet specified.
– j = the reaction number, with M being the number of the lastreaction
• Dots over variable indicate flow rates (d/dt)
Nomenclature for Balance Equations
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Difference Material Balance: No Reaction
∑=
∆=−=∆ K
k
k system N N N N 1
12
∑=
∆=−=∆ K
k
k t t system M M M M 1
12
• Mass:
• Mole:
( )∑=∆=∆
C
ik ik M M
1
where
( )∑=
∆=∆C
i
k ik N N 1
where
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Differential Material Balance: No Reaction
∑=
= K
k
k
system M
dt
dM
1
• Mass:
• Mole:
∑==
K
k
k system N dt
dN 1
( )∑==
C
ik ik M M
1
where
( )∑=
=C
i
k ik N N 1
where
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• We can write general chemical reaction balancesas:
• Where the Greek letters are the Stoichiometriccoefficients (positive for products; negative for
reactants); so that:
• Molar Extent of Reaction(X, Χ, etc.)
– N i,0 is the initial (before reaction)amount, N i is at any time.
– It is the same no matter what species you follow (evenif different stoich. amounts initially)
Notation for Chemical Reactions:
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• Overall
• Species:
Difference: Material & Species: w/Reaction
( )
( )
∑∑∑∑
∑∑
== ==
==
∆=∆Χ+∆=−=∆
∆=∆∆=−=∆
C
i k ik
C
i
M
j j ji
K
k k t t system
C
ik ik
K
k
k t t system
N N N N N N
M M M M M M
11 1,
1
11
12
12
ν
( )
( ) ∑∑∑∑
==
==
Χ+∆=−=∆
Χ+∆=−=∆
M
j
j ji
K
k k it it ii
M
j j jii
K
k k it it ii
N N N N
MW M M M M
1
,
1
,,
1,
1,,
12
12
ν
ν
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• Internal Energy: U
• The energy associated with the motion andinteractions of Molecules
– U: Microscopic Energy
• as opposed to “External” Energy which are
the whole Objects/Systems that are in motionor are in a potential field (electrical, magnetic,gravitational, etc.)
– Associated with the system’s “center of mass”
– Includes Kinetic and Potential
• Total Energy, E , would include the effects ofthe Internal and “External” Energy
– Total Energy = Internal Energy + Kinetic Energy +Potential Energy
Internal Energy & Total Energy
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• Heat • Heat may be defined as energy in transit
which flows naturally (no work) from a
higher temperature object to a lower
temperature object. – An object does not possess "heat";
– the appropriate term for the microscopic
energy in an object is internal energy.
– The internal energy may be increased by
transferring energy to the object from a higher
temperature (hotter) object - this is properly
called heating.
“Heat”
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/
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• Conservation of Energy:• The total energy change of a system is composed of
internal energy (molecular behavior) and external energy(kinetic and potential of the center of mass of the system)changes
• In addition, the system may change due to the heat flows,work flows, and mass flows; Mass flows have with their
accompanying enthalpy, and kinetic and potential energy.
– For closed System only
– When kinetic and potential energy of the system are negligible:U=E
1st Law of Thermodynamics
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• Open system bounded by a σ –surface
– 1 or many Mass Entrances/Exits,
• K = number of entrances/outlets – Total Work, W
• There may be several sources, shaft, PV, electrical: W= W s –
PdV+…
– Total Heat, Q
– Volume and surface area may change/deform (dV, d σ )
Generalized Open Systems
Q
W
σdM in, v in, z in
dM out , v out , z out
Wsσ : surface area
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• There are two Types of Internal Energy
that we need to keep track of:
• the U of the entire system vs. the U of the
plugs of mass coming in and out
• Each plug of mass has its own internal
energy, kinetic energy and potential energy
• The system U is a function of the ins and
out and the remainders and/or reactions
Internal Energy: Total vs. Flows
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• If Work or Heat flow INTO the system then
the value is POSITIVE
• If Work or Heat flow OUT the system then
the value is NEGATIVE
• Work: Shaft Work & System Boundary
Work of σ-Surface
– Shaft work : Mechanical Work, W s
– system boundary (volume) being move bypressure aka PV-work
Work & Heat and Signs
PdV W −=
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• To simplify the Balance, especially for what is
usually one of the dominant terms, U , weuse/define a new Thermodynamic Variable
• Enthalpy: H
• H = U +PV – It is similar to U, but with “built in” flow work
associated with it.
– Do not jump to conclusions that H can only beused with flow systems, it is a thermodynamic
property of all matter in all conditions
Enthalpy, H
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• Difference: mass/mole
• Differential: mass/mole
1st Law: Energy Balance: with Enthalpy, H
∑
∑
=
=
++++=
++=
++++=
++=
K
k
k k
k k k
system
K
k k
k
k k
system
gz v
MW H N W Q gz v
MW N U dt
d
dt
dE
gz
v
H M W Q gz
v
M U dt
d
dt
dE
1
22
1
22
22
2ˆ
2
∑
∑
=
=
++∆++=
++∆=∆
++∆++=
++∆=∆
K
k k
k
k k k
syst
K
k
k k
k k
syst
gz
v
MW H N W Q gz
v
MW N U E
gz v
H M W Q gz v
M U E
1
22
1
22
22
2ˆ
2
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MEB Summary: Difference:
( )
∑
∑∑
=
==
++∆++=
++∆=∆
∆=∆∆=−=∆
K
k k
k
sys
system
C
ik ik
K
k
k system
gz v
MW H N W Q gz v
MW N U E
N N N N N N
1
22
11
12
22
( )
∑
∑∑
=
==
++∆++=
++∆=∆
∆=∆∆=−=∆
K
k k
k system
C
ik ik
K
k
k t t system
gz v
H M W Q gz v
M U E
M M M M M M
1
22
11
2ˆ2
12
• Mass:
• Mole:
Non reacting systems
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