Lecture 41

Chapter 5p- Review Equations of State (chapter 4, briefly)- Thermodynamic Web (or network for transformations)

Departure Functions- Departure Functions

Maxwell Relations + Other Useful Ones2

PT

sh

vs sP

vT

5.16PP

p TsT

ThC

5.30

Ps sv

PT

5.17vv

v TsT

TuC

5.28

vT TP

vs

5.18PT

vv

1 5.26

vT

vs

5.19

P

Pv

1 5.27

PT TP

TPv

Uses for Maxwell Relations3

PC dvTPdT

TCds

v

v

dvPTPTdTCdu

vv

Example

ddixon

Pencil

Other Relations6

Other Relations7

vPvP T

PTvTCC

Real gas/fluid

RCC vP Ideal gas

KinTwithETDTCTBTAR

CP 322

Departure Functions8

For convenience. Also called “Residual Functions”: ..GIPTPT

depPT hhh ,,, PTPTPT

depPT

gasidealPP

gasidealTT

depPT hhhhhh 12 PTPPTTPT 22212111 ,,12

Departure Function Calculations9

A) Z Data or Equation of State

PdP

TZT

TRh

P

Pdep

0

eqn 6.46, p209, 7th ed. Smith, VanNess, Abbott

P0

0231 32223 BBABZBBAZBZ

Peng-Robinson EOS – S. Sandler, “Chemical & Engineering Thermodynamics”, 3rd ed., Wiley (1999)

BZBZ

b

adTdaT

ZRThdep

2121ln

221 BZb 2122

Lee-Kesler EOS can be used to calculate Z, as before.,

Departure Function Calculations10

B) Generalized compressibility results:

1

Pr,

0

Pr,

depTr

depTr

dep

TRh

TRh

TRh

(0) and (1) from:-Tables orCharts ccc TRTRTR -Charts

Departure Function Calculations11

C) Generalized Charts:

Departure Function Calculations12

C) Generalized Charts: ---use caution

Departure Function Calculations13

D) Data:

D) Data:

Joule-Thomson Expansion14

Throttle gas through a porous plug or valve.

Joule-Thomson Expansion15

T

hJT P

T

llP

JTZRT

vTvT

P

realP

realP

JT TPCC

Joule-Thomson Expansion16

Data from Perry’s Chemical Engineers Handbook

Joule-Thomson Applications17

Problem Solving Exercise19

Example

21

Example

Example

Example

Departure Function Calculations25

D) Data:

D) Data: