Notesale: Turn your study into money

Document Preview

Extracts from the notes are below, to see the PDF you'll receive please use the links above

---

1

CH-107

Lecture

6

CHEMICAL
ENGINEERING
THERMODYNAMICS-I
Dr
...
M Smith, 7th Edition
...

• “Thermodynamics, an Engineering
Approch” by Yunus A Cengel
...


CHEMICAL ENGINEERING THERMODYNAMICS-I

2

Faculty of Chemical Engineering, NEDUET

Lecture Outline
Equation of State (EOS)
...


Van der Waals Equation of State

3

CHEMICAL ENGINEERING THERMODYNAMICS-I

Faculty of Chemical Engineering, NEDUET

EOS

Equation of State (EOS)
 The molecules have no extension in space (i
...
,they
possess zero volume)
 The molecules donot interact with each other

...

 Intermolecular interactions are not only attractive
...

CHEMICAL ENGINEERING THERMODYNAMICS-I

4

Faculty of Chemical Engineering, NEDUET

EOS

Intermolecular Potential
 To account for nonideal gas behavior, we want to
describe how the intermolecular potential energy
depends on the position between molecules
...
molecular
separation is called a potential function
...

 There are many models of potential functions that are
used to approximate the relation between
intermolecular energy and position
...


5

CHEMICAL ENGINEERING THERMODYNAMICS-I

Faculty of Chemical Engineering, NEDUET

EOS

Lennard-Jones (LJ) 12/6 pairpotential
B/ r 12

A/r 6

A plot of the Lennard-Jones potential
function
...
As illustrated in
Figure, the energy parameter, eta, is given
by the depth of the potential well, while the
distance parameter, sigma, is given by the
distance at which attractive and repulsive
potentials are equal and is characteristic of
the molecular size
...

interaction force comes into play due to
overlap of the electron clouds of each
molecule, which results in a repulsive force
field between them
...

 The r-12 term represents the repulsive interaction, whereas the
term r-6 corresponds to the attractive interaction potential
...

 Since gases behave ideally at low pressures, intermolecular
separation distances therein are typically much higher than the
range over which intermolecular interactions are significant
...

7

CHEMICAL ENGINEERING THERMODYNAMICS-I

Faculty of Chemical Engineering, NEDUET

EOS

Cubic Equations of State for Gases
 Several equations have been proposed to represent
the P-v-T behavior of substances accurately over a
larger region with no limitations
...

 To obviate this problem an entire range of alternate
EOSs, termed cubic EOS, have been proposed by
various workers
...

CHEMICAL ENGINEERING THERMODYNAMICS-I

8

Faculty of Chemical Engineering, NEDUET

EOS

Cubic Equations of State for Gases
Such an EOS provides two distinct advantages
over many other more complex EOS
Found in the literature ; they allow:

1)Prediction of both gas and liquid(saturated)
phase molar volumes
2)Provide at rade-off between complexity and
accuracy of prediction
3)Non-zero volumes of gas particles
...

CHEMICAL ENGINEERING THERMODYNAMICS-I

9

Faculty of Chemical Engineering, NEDUET

EOS

Van der Waals Equation of State
The first of such cubic EOS was proposed by the Dutch
physicist Johannes Diderik vanvder Waals in 1873, and
has the following form:

10

CHEMICAL ENGINEERING THERMODYNAMICS-I

Faculty of Chemical Engineering, NEDUET

EOS

Van der Waals Equation of State

11

CHEMICAL ENGINEERING THERMODYNAMICS-I

Faculty of Chemical Engineering, NEDUET

EOS

Van der Waals Equation of State
What is (𝐯−𝐛)?
Gas molecules behave like small, impenetrable spheres
 Actual volume available for gas smaller than volume of
container, V
 Reduction in volume proportional to amount of gas, n
 Let another constant, b, relate amount of gas,n ,to
reduction in volume
 Volume term in ideal gase quation,V, becomes (V-b)
 Real world significances:
 Constants a and b depend on the gas identity
 Relative values of a and b can give a rough comparison
of properties of both gases

12

CHEMICAL ENGINEERING THERMODYNAMICS-I

Faculty of Chemical Engineering, NEDUET

EOS

Van der Waals Equation of State
Attractive effect (Pressure correction interms of
volume)

3

r=V

The B/ r−12 term represents the repulsive interaction,
−6
whereas the term a/r corresponds to the attractive
interaction potential

---