Revision on Important Concepts

8/10/2019 Revision on Important Concepts

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Revision on Important Concepts

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2/16

2


3/16

3

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


4/16

4

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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5

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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6

Ans. 331.2 K, y 1 = 0.67, y 2 = 0.33


7/16

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

+

=


8/16

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.


9/16

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 +=


10/16

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 ,,


11/16

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


12/16

Solution ThermodynamicsPartial property for binary system at const T & P

121 dx

dM x M M +=

112 dx

dM x M M =


13/16

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 ,,,,


14/16

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,


16/16

16

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%

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Revision on Important Concepts