CHAPTER 8
BALANCES ON NONREACTIVE PROCESSES
By : Ms. Nor Helya Iman Bt Kamaludin
Email: helya@unimap.edu.my
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PTT 108: Mass and Energy Balances
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
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Different symbols between close and open system
CLOSE SYSTEM
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OPEN SYSTEM
n (amount)
(molar flow rate)
U (internal energy)
(rate of enthalpy)
Û (specific internal energy)
(specific enthalpy)
PTT 108: Mass and Energy Balances
Introduction (cont’d)
 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 ˚C and 1 atm converted to
phenol vapor at 300 ˚C and 3 atm.
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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)Chapter 9
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PTT 108: Mass and Energy Balances
Hypothetical Process Path
 State properties

Properties that depend on the state of the species (primarily on
its temperature and state of aggregation, and also
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.
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PTT 108: Mass and Energy Balances
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 for Phenol : P= 1 atm; Tm= 42.5˚C and Tb=
181.4˚C
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PTT 108: Mass and Energy Balances
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 (open system)

For closed system, construct a table with columns for initial and
final amounts of each species (mi or ni) and specific internal
energies relative to the chosen reference states (Ûi) .

For an open system, construct a table with columns for inlet
and outlet stream component flow rates (
) and
specific enthalpies relative to the chosen references states (Ĥi).
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PTT 108: Mass and Energy Balances
Procedure Energy Balance Calculations (cont’d)
5. Calculate all required values of Ĥi or Ûi and insert the
values in the appropriate places in the table.
6. Then calculate ΔĤ or ΔÛ for the system.
Closed System:
Open System:
7. Calculate any work, kinetic energy, or potential
energy terms that you have not dropped from the energy
balance.
8. Solve the energy balance for whichever variable is
unknown (often Q or ).
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PTT 108: Mass and Energy Balances
Class Discussion
EXAMPLE 8.1-1: Energy Balance on a Condenser
The flowchart
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PTT 108: Mass and Energy Balances
Solution
STEP 1: Perform required material balance calculations.
-None are required in this example because there are no
material balance involved in this process.
STEP 2: Write and simplify the energy balance.
For open steady-state system:
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PTT 108: Mass and Energy Balances
 Delete any of the terms that are either zero or negligible in
process system.
-No moving parts and no energy is transferred in the system:
-No significant vertical distance separates the inlet and outlet
ports:
-Phase changes and nonnegligible temperature changes occur:
So, the energy balance become:
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PTT 108: Mass and Energy Balances
STEP 3: Choose reference states for acetone and nitrogen.
N2 (g, 25˚C, 1 atm) : convenient (Table B.8)
Ac (l, 20˚C, 5 atm) : choose from one of the process stream.
STEP 4: Construct an inlet-outlet enthalpy table.
References: Ac (l, 20˚C, 5atm); N2 (g, 25˚C, 1atm)
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STEP 5: Calculate all unknown specific enthalpies
In this step we need to find
i.
For changes in pressure (∆P) at constant T
ii.
For changes in temperature (∆T) at constant P
iii. For changes in phases at constant P and T
Use heat of vaporization
or heat of melting
normal boiling point and normal melting point,
respectively. (can be obtained from Table B.1)
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at
 The process path involved for determination of
= (0.0297 + 4.68 + 30.2 + 0.753) kJ/mol
= 35.7 kJ/mol
*Use the same manner to obtain the values for
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-insert all specific enthalpies into inlet-outlet enthalpy table
STEP 6: Calculate
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PTT 108: Mass and Energy Balances
STEP 7: Calculate nonzero work, kinetic energy and potential
energy terms
-no need to be calculated since there are no shaft work and we
are neglecting kinetic and potential energy.
STEP 8: Solve the energy balance for
= -2320 kJ/s
= -2320 kW
Heat must be transferred from the condenser at a rate of -2320
kW to achieve the required cooling and condensation.
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PTT 108: Mass and Energy Balances
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
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PTT 108: Mass and Energy Balances
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:
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Changes in T and Constant P
(no phase change or reactions)
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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:
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Heat Capacity Formulas
Definition:
Heat capacities, Cp and Cv are physical properties of materials
and are tabulated in standard references.
Units:
J/(mol.K) and Btu/(lbm.˚F)
Relationships exist between Cp and Cv :
where R = gas constant
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PTT 108: Mass and Energy Balances
Heat capacity, Cp
Estimation of heat capacities, Cp
 Kopp’s rule- simple empirical method for estimating Cp of
solid or liquid at or near 20˚C 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
 Polynomial expressions for Cp in Table B.2 based on the
experimental data for the listed compound.
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PTT 108: Mass and Energy Balances
Heat capacity, Cp (cont’d)
 Table B.2 demonstrated the heat capacities as a function
of temperature (at low pressures) in the equation form
for a number of solid, liquid, and gaseous substances.
This is your source of ideal-gas heat capacities.
 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.
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PTT 108: Mass and Energy Balances
Heat capacity, Cp (cont’d)
Mixtures:
Where
= heat capacity of the mixture
= mass or mole fraction of the ith component
= heat capacity of the ith component
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PTT 108: Mass and Energy Balances
Class Discussion
 EXAMPLE 8.3-1
 EXAMPLE 8.3-2
 EXAMPLE 8.3-3
 EXAMPLE 8.3-4
 EXAMPLE 8.3-5
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PTT 108: Mass and Energy Balances
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 transition of a substance from
one phase to another at constant T & P.
 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 vapor forms 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.

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PTT 108: Mass and Energy Balances
Estimation of Heat of Vaporization
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1.
Trouton’s rule – accuracy between 30%
2.
Chen’s equation – accuracy between 2%
3.
Clausius-Clapeyron equation - plot In p* versus 1/T
PTT 108: Mass and Energy Balances
Estimation of Heat of Vaporization (cont’d)
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
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PTT 108: Mass and Energy Balances
Class Discussion
 EXAMPLE 8.4-1
 EXAMPLE 8.4-2
 EXAMPLE 8.4-3
 EXAMPLE 8.4-4
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PTT 108: Mass and Energy Balances
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 AirWater system and normally is at Pressure of 1 atm.
 Psychrometric Chart is very useful in the analysis of
humidification, drying, and air-conditioning process.
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PTT 108: Mass and Energy Balances
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Psychrometric Charts (cont’d)
 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 – 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.
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PTT 108: Mass and Energy Balances
Psychrometric Charts (cont’d)
 Relative humidity, hr
Curves on the psychrometric chart correspond to specified
values of hr (100%, 90%, 80%, etc.). The curve that form the
left boundary of the chart is 100% relative humidity
(saturation curve).
 Dew point, Tdp
The temperature at which humid air becomes saturated if it
is cooled at constant pressure.
 Humid volume,
(m3/kg dry air)
The humid air is the volume occupied by 1 kg of dry air plus
the water vapor that accompanies it.
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PTT 108: Mass and Energy Balances
Class Discussion
 EXAMPLE 8.4-5
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THANK YOU….
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PTT 108: Mass and Energy Balances