Chapter 8
Energy Balance on
Nonreactive Species
Introduction
• 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.
• Method to calculate ΔĤ and ΔÛ associated with certain process
such as:
1. Change in P, at constant T & constant state of aggregation
2. Change in T, at constant T & constant state of aggregation
3. Phase changes at constant T & constant P
4. Mixing at constant T & constant P
5. Chemical reaction at constant T & constant P
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.
Hypothetical Process Path
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
True Path
Ph (s, 25C, 1 atm)
Change T, Constant P & Phase
Ph (s, 42.5C, 1 atm)
Change Phase, Constant P & T
Ph (l, 42.5C, 1 atm)
Change T, Constant P & Phase
Ph (l, 181.4C, 1 atm)
Ĥ 1
Ĥ
Ĥ 6
Ĥ 2
Ĥ 3
Ph (v, 300C, 3 atm)
Change P, Constant T & Phase
Ph (v, 300C, 1 atm)
Ĥ 4
Ĥ 5
Change T, Constant P & Phase
Ph (v, 181.4C, 1 atm)
Change Phase, Constant P & T
Hˆ  Hˆ 1  Hˆ 2  Hˆ 3  Hˆ 4  Hˆ 5  Hˆ 6
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.
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)
Inlet
Substance
Ac (v)
Ac (l)
N2
Outlet
n in
Ĥ in
n out
Ĥ out
66.9
Ĥ 1
3.35
Ĥ 2
-
-
63.55
0
33.1
Ĥ 3
33.1
Ĥ 4
Change in P at Constant T &
Constant Phase
1.Solid & Liquid
- nearly independent of pressure
Uˆ  0
Hˆ  VˆP
2.Ideal Gases
-independent of pressure ( unless undergo
very large pressure changes)
Uˆ  0
ˆ 0
H
Change in T at Constant P &
Constant Phase
• Sensible heat – heat that must be transferred to RAISE or
LOWER the temperature of substance or mixture of
substance
– Cp - heat capacity at constant pressure
- given in Table B.2 in the form of polynomial
equation function of temperature
– Cv - heat capacity at constant volume
C p  Cv
C p  Cv  R
Liquid & Solid
Ideal Gas
• Specific internal energy change
T2
Uˆ   C v (T )dT
T1
Ideal gas
: exact
Solid or Liquid : good approximation
Nonideal gas
: valid only if V is constant
Change in T at Constant P &
Constant Phase
• Specific enthalpy change
T2
ˆ
H   C p (T )dT
T1
Ideal gas
: exact
Nonideal gas : exact only if P is
constant
T2
ˆ
ˆ
H  VP   C p (T )dT
T1
Solid & Liquid
Heat Capacities, 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
• Estimation for heat capacities of mixtures
(C p ) mix (T )   yi C pi (T )
Cpi
yi
= Cp for ith component
= mass or moles fraction
CLASS DICUSSION
EXAMPLE
EXAMPLE
EXAMPLE
EXAMPLE
8.3-1
8.3-2
8.3-3
8.3-4
CLASS DICUSSION
EXAMPLE 8.1-1
EXAMPLE 8.3-5
EXAMPLE 8.3-6
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.
CLASS
DISCUSSION
EXAMPLE 8.4-1
EXAMPLE 8.4-2
Estimation of Heat of
Vaporization
1. Trouton’s rule – accuracy between 30%
Hˆ v (kJ / mol )  0.088Tb
Hˆ (kJ / mol )  0.109T
v
b
nonpolar liquid
water or low MW alcohol
2. Chen’s equation – accuracy between 2%
Tb [0.0331(Tb / Tc )  0.0327  0.0297 log 10 Pc ]
ˆ
H v (kJ / mol) 
1.07  (Tb / Tc )
3. Clausius-Clapeyron equation - plot In p* versus 1/T
Hˆ v
In p  
B
RT
*
Estimation of Heat of
Vaporization
4. Chaperon equation
Hˆ v
d ( In p * )

d (1 / T )
R
5. Watson correlation – estimate ΔĤv at T2 from known
ΔĤv at T1
0.38
 Tc  T2
ˆ
ˆ
H v (T2 )  H v (T1 )
 Tc  T1



Estimation of Heat of Fusion
ΔĤm (kJ/mol) = 0.0092 Tm (K)
= 0.0025 Tm (K)
= 0.050 Tm (K)
metallic elements
inorganic compound
organic compound
CLASS
DICUSSION
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.
ANY QUESTION?
29 March 2007