COURSE WORKBOOK
CHE 205: Materials and Energy Balances
By AraOluwa Adaramola ()
,NOTE TO STUDENTS
These discussion notes are a supplementary learning resource that summarizes key
concepts in this course, models problem solving using worked examples, and provides
space for problem solving. Some features of this resource include:
• Brown text highlighting important information
• Learning objectives to guide your learning process and check your understanding
• Fully and partially worked example problems
• Blank pages for handwritten notes and additional problem solving
2
,TABLE OF CONTENTS
PROBLEM SOLVING CONCEPTUAL FRAMEWORK............................................................................... 4
SECTION 1: MATERIALS BALANCES ...................................................................................................... 5
Learning Objectives ............................................................................................................................ 8
1.1 INTRODUCTION TO MATERIALS BALANCES ........................................................................................... 10
1.2 PROCESS CLASSIFICATION ................................................................................................................. 15
1.3 MATERIALS BALANCES ....................................................................................................................... 17
1.4 MATERIALS BALANCES AND CHEMICAL REACTIONS .............................................................................. 42
DOF Analysis on systems with chemical reactions ........................................................................... 43
Independent Species and Reactions ............................................................................................... 43
1.5 MATERIALS BALANCES AND COMBUSTION REACTIONS ......................................................................... 64
SECTION 2: INTRODUCTORY THERMODYNAMICS ............................................................................. 72
Learning Objectives .......................................................................................................................... 73
2.1 THE FIRST LAW OF THERMODYNAMICS ................................................................................................ 76
State Property ................................................................................................................................... 76
First Law of Thermodynamics ........................................................................................................... 76
Enthalpy ............................................................................................................................................ 76
2.2 SINGLE-PHASE SYSTEMS: SOLIDS AND LIQUIDS...................................................................... 78
Solids and Liquids ............................................................................................................................. 78
2.3 SINGLE-PHASE SYSTEMS: GASES .............................................................................................. 80
Non-Ideal Equations of State ............................................................................................................ 91
2.4 MULTIPHASE SYSTEMS ................................................................................................................ 99
Thermodynamic Equilibrium ............................................................................................................ 100
Gibbs Phase Rule ........................................................................................................................... 100
Gas-Liquid Equilibrium Systems ..................................................................................................... 104
SECTION 3: ENERGY BALANCES........................................................................................................ 119
Learning Objectives ........................................................................................................................ 120
3.1 CLOSED SYSTEM ENERGY BALANCE ................................................................................................. 122
Closed System Energy Balance ...................................................................................................... 123
3.2 OPEN SYSTEM ENERGY BALANCE ..................................................................................................... 129
Open System Energy Balance ........................................................................................................ 130
3.3 CHANGES IN ENTHALPY AND INTERNAL ENERGY ................................................................................ 138
State Changes ................................................................................................................................ 138
Changes in Pressure (at Constant Temperature) ........................................................................... 141
Changes in Temperature (at Constant Pressure) ........................................................................... 141
Phase Changes ............................................................................................................................... 142
Steam Tables .................................................................................................................................. 142
Mixing and Solution ......................................................................................................................... 156
Chemical Reactions ........................................................................................................................ 161
SECTION 4: TRANSIENT STATE BALANCES ..................................................................................... 179
Learning Objectives ........................................................................................................................ 179
4.1 CLOSED SYSTEM ENERGY BALANCES ............................................................................................... 180
Differential Balance ......................................................................................................................... 180
Mass Balances at Transient State .................................................................................................. 181
Energy Balances at Transient State ................................................................................................ 189
3
, Problem Solving Conceptual Framework
The following conceptual framework illustrates a general problem-solving approach for
chemical engineering problems related to materials and energy balances. A problem
statement will provide some information about the process (data). Additional information
may be obtained from other sources (i.e., engineering tables). From the problem
statement and relevant chemical engineering knowledge, chemical engineers create an
appropriate model that identifies the unknown and known variables, as well as the
relevant relationships. An effective problem-solving approach will apply the data,
assumptions, and model to correctly solve the materials and energy balances. At the
end, check that the derived solution makes sense to ensure that your model works as
intended.
4
CHE 205: Materials and Energy Balances
By AraOluwa Adaramola ()
,NOTE TO STUDENTS
These discussion notes are a supplementary learning resource that summarizes key
concepts in this course, models problem solving using worked examples, and provides
space for problem solving. Some features of this resource include:
• Brown text highlighting important information
• Learning objectives to guide your learning process and check your understanding
• Fully and partially worked example problems
• Blank pages for handwritten notes and additional problem solving
2
,TABLE OF CONTENTS
PROBLEM SOLVING CONCEPTUAL FRAMEWORK............................................................................... 4
SECTION 1: MATERIALS BALANCES ...................................................................................................... 5
Learning Objectives ............................................................................................................................ 8
1.1 INTRODUCTION TO MATERIALS BALANCES ........................................................................................... 10
1.2 PROCESS CLASSIFICATION ................................................................................................................. 15
1.3 MATERIALS BALANCES ....................................................................................................................... 17
1.4 MATERIALS BALANCES AND CHEMICAL REACTIONS .............................................................................. 42
DOF Analysis on systems with chemical reactions ........................................................................... 43
Independent Species and Reactions ............................................................................................... 43
1.5 MATERIALS BALANCES AND COMBUSTION REACTIONS ......................................................................... 64
SECTION 2: INTRODUCTORY THERMODYNAMICS ............................................................................. 72
Learning Objectives .......................................................................................................................... 73
2.1 THE FIRST LAW OF THERMODYNAMICS ................................................................................................ 76
State Property ................................................................................................................................... 76
First Law of Thermodynamics ........................................................................................................... 76
Enthalpy ............................................................................................................................................ 76
2.2 SINGLE-PHASE SYSTEMS: SOLIDS AND LIQUIDS...................................................................... 78
Solids and Liquids ............................................................................................................................. 78
2.3 SINGLE-PHASE SYSTEMS: GASES .............................................................................................. 80
Non-Ideal Equations of State ............................................................................................................ 91
2.4 MULTIPHASE SYSTEMS ................................................................................................................ 99
Thermodynamic Equilibrium ............................................................................................................ 100
Gibbs Phase Rule ........................................................................................................................... 100
Gas-Liquid Equilibrium Systems ..................................................................................................... 104
SECTION 3: ENERGY BALANCES........................................................................................................ 119
Learning Objectives ........................................................................................................................ 120
3.1 CLOSED SYSTEM ENERGY BALANCE ................................................................................................. 122
Closed System Energy Balance ...................................................................................................... 123
3.2 OPEN SYSTEM ENERGY BALANCE ..................................................................................................... 129
Open System Energy Balance ........................................................................................................ 130
3.3 CHANGES IN ENTHALPY AND INTERNAL ENERGY ................................................................................ 138
State Changes ................................................................................................................................ 138
Changes in Pressure (at Constant Temperature) ........................................................................... 141
Changes in Temperature (at Constant Pressure) ........................................................................... 141
Phase Changes ............................................................................................................................... 142
Steam Tables .................................................................................................................................. 142
Mixing and Solution ......................................................................................................................... 156
Chemical Reactions ........................................................................................................................ 161
SECTION 4: TRANSIENT STATE BALANCES ..................................................................................... 179
Learning Objectives ........................................................................................................................ 179
4.1 CLOSED SYSTEM ENERGY BALANCES ............................................................................................... 180
Differential Balance ......................................................................................................................... 180
Mass Balances at Transient State .................................................................................................. 181
Energy Balances at Transient State ................................................................................................ 189
3
, Problem Solving Conceptual Framework
The following conceptual framework illustrates a general problem-solving approach for
chemical engineering problems related to materials and energy balances. A problem
statement will provide some information about the process (data). Additional information
may be obtained from other sources (i.e., engineering tables). From the problem
statement and relevant chemical engineering knowledge, chemical engineers create an
appropriate model that identifies the unknown and known variables, as well as the
relevant relationships. An effective problem-solving approach will apply the data,
assumptions, and model to correctly solve the materials and energy balances. At the
end, check that the derived solution makes sense to ensure that your model works as
intended.
4
