revision on important concepts
TRANSCRIPT
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8/10/2019 Revision on Important Concepts
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Revision on Important Concepts
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111 RT V P =
2211 V PV P
=
Check the right unit to use for P and T when R = 8.314 J/mol.K is used.
Given
Find P 2 using the following equation (revise polytropic process)
Calculate W using the equation given but ensure the right unit is used so that W is in J.Then find internal energy using first law.
12 2V V =
W QU +=0
Ans. 1499.8 J
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1
2
1
2 lnlnPP
RT T
C S P =
1
2
1
2 lnlnV V
RT T
C S V +=
Or, derive the following equation from dS = dQ/T and dU = dQ + dW
Important: Do not assume 1 mol. Check if amount or volume is informed.
In this case, calculate the no. of mole since volume is given.nRT PV t =
( )12 T T nC U V = Ans. 20.79 J/K for both (a) and (b)
Note that the work from stirrer is not the same as the work of gas. Do
not assume W = 0 for part (b) stirrer gas W W QW QU ++=+=
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There are many ways to prove this equation.You may start with either of the following together with use of Maxwells equations.
( )
dV
V
U dT
T
U dU
V T U U
T V
+
=
= ,
PdV TdS dU =
( )
dV V
S dT
T
S dS
V T S S
T V
+
=
= ,
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Ans. 331.2 K, y 1 = 0.67, y 2 = 0.33
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BUBL P / DEW P Calculation
7
sat sat P xP xP 222111 +=
sat iiii P xP y: Laws Raoult' Modified =
sat sat P y
P y
P
22
2
11
1
1
+
=
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BUBL T Calculation
(1. by iteration to convergence)
Pconstant given ,T xT xT byT initial Estimate1. sat 22sat
11 +=
T initial from /PPand , , A,Find 2. sat 2sat
121
ii
isat i C P A
BT
=
ln
/ 2211 x xP
P
fromP newFind 3.
sat 1
sat 1
+=
equation Antoineinto3Step fromPinsertingbyT newFind 4. sat 1
T new fromvaluesthose find but 2Stepto Return5.
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BUBL T Calculation
(2. by trial)
Pconstant given ,T xT xT byT initial Estimate1. sat 22sat
11 +=
T initial fromPand P , , A,Find 2. sat 2sat
121
ii
isat i C P A
BT
=
ln
Pgiventoequalisit if seetoequationP BUBLintoubstituteS 3.
3)Step fromPcalculated on(dependingT newareguessnot, If 4.
sat sat P xP xP 222111 +=
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Solution ThermodynamicsChemical potential (by definition)
the change in energy when an infinitesimal number of particles ofspecies i is added at const T & P
At equilibrium,Partial property (by definition)
Measure of response of total property nM to the addition at const T & Pof a differential amount of species i to a finite amount of solution
ii =
( ) jnPT i
i nnG
,,
( ) jnPT i
i nnM
M ,,
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Solution Thermodynamics
Total property from summability relation
Gibbs/Duhem equation
Must be satisfied for all changes in P, T, and partial property in ahomogeneous phase
=i
ii M x M
dT T
M dP
P M
M d x
xP xT i
ii
,,
+
=
P)&T const (at 0 M d xi ii =
( ) ,... ,...,n ,nT,P,n nM i21= From
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Solution ThermodynamicsPartial property for binary system at const T & P
121 dx
dM x M M +=
112 dx
dM x M M =
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Solution ThermodynamicsParallelism
Ideal gas mixture model: Gibbs theorem
Apply to get partial properties from pure-species properties
Combined with summability relation to get solution properties
( ) iii V PU H vs. nV PnU nH +=+=
( ) ( ) igiigiiigiigi V M that provided pT M PT M = ,,
igi
igi
igi
igi
igi
igi GS H fromGS H Calculate ,,,,
igi
igi
igi
igigig GS H fromGS H Calculate ,,,,
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Solution ThermodynamicsFugacity, f vs. fugacity coefficient, = f /P
For an ideal gas, f = P and = f /P = 1For a real gas, f = P (for simplicity, i is omitted)
Knowing
At any P, use cubic equations of state
or generalized correlation for Z
At low to moderate P, use generalized correlation for B( )( ) 10=
( )+= 10
exp B BT P
r
r
( )P
dP Z
RT
G P R
==
01ln
( ) qI Z Z = ln1ln
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Solution ThermodynamicsFugacity, f vs. fugacity coefficient, = f /P
For an ideal gas, f = P and = f /P = 1For a real gas, f = P (for simplicity, i is omitted)For a pure liquid,
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vnvn
nn
yo
iioii +
+==
+
+==
j j j
j j jiiii vn
vn
nn
y
0
,0 (multireaction)i = species
j = reaction index
(single reaction)
K PP
y iiii
= o)( K x iiii
= )(Ans. 70%