Mass and Energy Balance

ERT 214

Semester 1

Course Details

Mass and Energy Balance / Kesimbangan Bahan dan Tenaga

Credit hours : 4

Contact hours: 3 hours (L), 3 hours (P), 1 hour (T) per week

Lecture : 42 hours per semester

Practical : 10 hours per semester

Tutorial : 18 hours per semester

Evaluation contribution:

Examinations = 70%

Final = 50%

2 Midterm Tests = 20%

Coursework = 30%

Assignments/Quizzes = 10%

Lab = 20%

Course Details (cont’d)

Course Outcomes (COs) will be covered

CO3 – Analyze energy balance problems and apply energy

balance concepts to solve problem in chemical and biological

systems

Courseworks

3 Assignments

3 Quizzes

1 Midterm Test 2

Class Participation

Course Details (cont’d)

Course Contents

Energy Balances on Nonreactive Processes (Wk 11)

Energy Balances on Reactive Processes (Wk 12)

Energy Balance for Biological Process System (Wk 13-14)

Unsteady state Material and Energy Balances (Wk 15)

Important Reminder

Attendance should not less than 80%, or else you

will be barred from taking final examination.

Plagiarism and copying other students’ work is

strictly prohibited especially in doing assignments

and lab reports, or else both parties will get zero.

Cheating in quizzes and examination is also

prohibited, or else both parties will get zero.

Therefore, study hard and smart. Take note of the

important chapters or things that will be highlighted

throughout lectures.

Chapter 3

Part 3 – Balances on Non-reactive

Processes

Week 11

Review on Material Balance

A fermentation slurry containing Streptomyces

kanamyceticus cells is filtered using a continuous

rotary vacuum filter. 120 kg h- 1 slurry is fed to the

filter; 1 kg slurry contains 60 g cell solids. To

improve filtration rates, particles of diatomaceous-

earth filter aid are added at a rate of 10 kg h- 1. The

concentration of kanamycin in the slurry is 0.05%

by weight. Liquid filtrate is collected at a rate of 112

kg h-1; the concentration of kanamycin in the

filtrate is 0.045% (w/w). Filter cake containing cells

and filter aid is continuously removed from the filter

cloth. What percentage liquid is the filter cake?

Review on Material Balance (cont’d)

Introduction

Non-reactive processes

Processes that undergo without chemical reaction

Depends on the physical / environmental factors like temperature,

volume, pressure, boiling and melting, as well as vaporization

Normally in chemical process unit, Ws=0; ΔEp=0; ΔEk=0; Then energy

balance equation become:

Close System Open System

Q=ΔU Q=ΔH

For this chapter, we will learn the procedure for evaluating ΔU and

ΔH when table Ĥ and Û are not available for all process species.

Example enthalpy change (ΔĤ) for solid phenol at 25 oC and 1 atm

converted to phenol vapor at 300 oC and 3 atm.

Introduction (cont’d)

To evaluate changes in enthalpy or internal energy, we can

make up any process path we want to simplify the

calculations. They can often be evaluated for:

1. changes in P at constant T

2. changes in T at constant P

3. changes in T at constant V

4. changes in phase at constant T and P (e.g., heats of

vaporization)

5. mixing at constant T and P (heats of mixing)

6. chemical reactions at constant T and P (heats of

reaction)

Hypothetical Process Path

State properties

properties that depend on the state of the species (primarily on

its temperature and state of aggregation, and to lesser extent on

its pressure).

Specific enthalpy (Ĥ) and specific internal energy (Û) are state

properties species

When a species passes from one state to another state, both ΔĤ

and ΔÛ for the process are independent of the path taken from

the first state to the second state.

We can construct a hypothetical process path which can consist of

several step based on our convenience, as long as we reach to the

final state starting from their initial state.

12ˆˆˆ HHH

Hypothetical Process Path (Examples)

ΔĤ= (vapor, 300˚C, 3 atm) – (solid, 25˚C, 1 atm)

Cannot determine directly form enthalpy table – must use hypothetical process

path consist of several step.

Check Table B.1 : P= 1 atm; Tm= 42.5C and Tb= 181.4C

654321ˆˆˆˆˆˆˆ HHHHHHH

True Path

1H

2H

3H

H

4H 5H

6H

Ph (s, 25C, 1 atm)

Ph (s, 42.5C, 1 atm)

Ph (l, 42.5C, 1 atm)

Ph (l, 181.4C, 1 atm) Ph (v, 181.4C, 1 atm)

Ph (v, 300C, 1 atm)

Ph (v, 300C, 3 atm)

Change T, Constant P & Phase

Change Phase, Constant P & T

Change T, Constant P & Phase

Change Phase, Constant P & T

Change T, Constant P & Phase

Change P, Constant T & Phase

Procedure Energy Balance Calculations

1. Perform all required material balance calculations.

2. Write the appropriate form of the energy balance (closed or open system) and delete any of the terms that are either zero or negligible for the given process system.

3. Choose a reference state – phase, temperature, and pressure – for each species involved in the process.

4. Construct inlet-outlet table for specific internal energy (close system) or specific enthalpy (close system)

For closed system, construct a Table with columns for initial and final amounts of each species (mi or ni) and specific internal energies (Û) relative to the chosen reference states

For an open system, construct a table with columns for inlet and outlet stream component flow rates (mi or ni) and specific enthalpies (Ĥ) relative to the chosen references states.

Procedure Energy Balance Calculations

5. Calculate all required values of Ĥ or Û and insert the values in the appropriate places in the table. Then calculate ΔĤ or ΔÛ for the system.

6. Calculate any work, kinetic energy, or potential energy terms that you have not dropped from the energy balance

7. Solve the energy balance for whichever variable is unknown (often Q)

Example of Inlet-Outlet Enthalpy Table

References: Ac (l, 20˚C, 5atm); N2 (g, 25˚C, 1atm)

Substance

Inlet Outlet

Ac (v) 66.9 3.35

Ac (l) - - 63.55 0

N2 33.1 33.1

inn outninH outH

1H 2H

4H3H

Changes in P at Constant T (no phase

change or reactions)

Ideal gases:

Independent of pressure ( unless undergo very large pressure changes)

Real gases:

must evaluate from:

1. enthalpy departure charts

2. an equation of state

3. tabulated data

Liquids and solids:

Nearly independent of pressure

0ˆˆ HU

0ˆ,0ˆ HU

PVHU ˆˆ,0ˆ

Changes in T and Constant P (no phase

change or reactions)

Called sensible heat, heat that must be transferred to RAISE

or LOWER the temperature of substance or mixture of

substance and we usually find:

Heat capacities help us calculate this change in enthalpy. The

“heat capacity at constant pressure” is defined by:

Thus, enthalpy changes at constant P are given by

integration of this equation:

HQ

P

pT

HC

ˆ

TCTTCdTCH pp

T

T

p 12

2

1

ˆ

Changes in T and Constant P (no phase

change or reactions)

Changes in T at Constant V (no phase

change or reactions)

Here, we use the heat capacity at constant volume, defined

by:

Ideal gases:

Liquids and solids:

dTCU

T

UC

T

T

v

V

v

2

1

ˆ

ˆ

RCC pv

pv CC

Heat capacity, Cp

Estimation of heat capacities, Cp

Kopp’s rule- simple empirical method for estimating Cp of

solid or liquid at 20OC based on the summation of atomic

heat capacities (Table B.10) of the molecular compound.

(Cp) Ca(OH)2 = (Cpa) Ca + 2 (Cpa) O + 2 (Cpa) H

= 26 + (2x17) + (2x9.6)= 79 J/mol.˚C

Heat capacity, Cp

Heat capacities as a function of temperature (at low pressures) are given in equation form for a number of solid, liquid, and gaseous substances in Appendix B.2, p. 635. This is your source of ideal-gas heat capacities.

The “mean heat capacity at constant pressure” has been introduced above. If values are available, it is much easier to use, because integration is not required.

Tables of specific enthalpies eliminate the need for use of heat capacities, i.e., someone has already done the integrations for you. For "combustion gases" you should use the tables of molar enthalpies given in Table B.8 and Table B.9.

Heat capacity, Cp

Mixtures:

This mole-fraction average relation is exact for

ideal gas mixtures, and approximately correct

for many liquid solutions.

i

pip CyC

Class Discussion

EXAMPLE 8.3-1

EXAMPLE 8.3-2

EXAMPLE 8.3-3

EXAMPLE 8.3-4

Phase Change Operations

Phase change such as melting and evaporation are usually

accompanied by large changes in internal energy and enthalpy

Latent heat

Specific enthalpy change associated with the phase at constant temperature and

pressure.

Heat of fusion or heat of melting, ΔĤm (T,P)

Specific enthalpy different between solid and liquid forms of species at T & P

Heat of solidification (liquid to solid) is –ve value of heat of fusion.

Heat of vaporization, ΔĤv (T,P)

Specific enthalpy different between liquid and vaporforms of species at T & P

Heat of condensation (vapor to liquid) is –ve value of heat of vaporization.

The latent heat of phase change may vary considerably with the

temperature at which the changes occurs but hardly varies with

the pressure at the transition point.

Estimation of Heat of Vaporization

1. Trouton’s rule – accuracy between 30%

2. Chen’s equation – accuracy between 2%

3. Clausius-Clapeyron equation - plot In p* versus 1/T

alcoholMW lowor water 109.0)/(ˆ

liquidnonpolar088.0)/(ˆ

bv

bv

TmolkJH

TmolkJH

)/(07.1

]log0297.00327.0)/(0331.0[)/(ˆ 10

cb

ccbbv

TT

PTTTmolkJH

BRT

HpIn v

ˆ*

Estimation of Heat of Vaporization

4. Chaperon equation

5. Watson correlation – estimate ΔĤv at T2 from known ΔĤv at T1

Estimation of Heat of Fusion

ΔĤm (kJ/mol) = 0.0092 Tm (K) metallic elements

= 0.0025 Tm (K) inorganic compound

= 0.050 Tm (K) organic compound

R

H

Td

pInd vˆ

)/1(

)( *

38.0

1

2

12 )(ˆ)(ˆ

TT

TTTHTH

c

cvv

Class Discussion

EXAMPLE 8.4-1

EXAMPLE 8.4-2

EXAMPLE 8.4-4

Psychrometric Charts

PSYCHROMETRIC chart (or HUMIDITY Chart) is a compilation of a large

quantity of physical property data in a single chart. The properties are:

(a) Wet Bulb Temperature

(b) Saturation Enthalpy

(c) Moisture Content

(d) Dry Bulb Temperature

(e) Humid Volume

The Psychrometric Chart is particularly important for Air-Water system

and normally is at Pressure of 1 atm.

Psychrometric Chart is very useful in the analysis of humidification, drying,

and air-conditioning process.

To use Psychrometric Chart, you need to know TWO

values to determine the values of the others on the chart.

IMPORTANT TERM:

Dry-bulb temperature, T – The abscissa of the chart. This is

the air temperature as measured by thermometer,

thermocouple, or other conventional temperature-

measuring device.

Absolute humidity, ha [kg H2O (v)/ kg DA] – Called

moisture content placed on the ordinate of the chart.

Psychrometric Charts