Process thermodynamics by sandler

8/14/2019 Process thermodynamics by sandler

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Chapter 1 IntroductoryMaterial



• 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



• 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



• 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



• 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



• 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



• 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



• 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



• 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



Chapter 2:

Conservation of Mass



• 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?



• 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



• 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



• 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



• 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



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



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



• 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:





• 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









• 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



• 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/





• 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



• 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



• 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



• 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 −=



• 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



• 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



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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Process thermodynamics by sandler