Chapter 6
Process energy calculations and
synthesis of safe and efficient
energy flow sheets
• Energy requirements of chemical processes:
T & P manipulation for fast reaction rate,
favorable reaction equilibrium, efficient
separation
• Energy balance equations and process
energy calculations
Energy balance equations
Accumulation = In - out
Materials
Energy
Energy balance equations
• No generation and consumption terms
• Only a total energy balance equation, not a component
energy balance
System energy, energy flows, specific energy
Energy transfer into the system in two ways
1. Through material transfer
2. Without material transfer
Energy flow across system boundaries
1. Materials flows in and out of the system
(open system)
2. Energy flows via heat or work
(closed system)
Energy of a system or stream
Specific system energy
Specific stream energy
• A function of the state of the system or stream
• State of a system can be identified by velocity, position,
P, T, phase, composition
• The numerical value depends on the chosen reference
state of a system
Quantification of Ê
• Method 1: find data on Ê of the material of interest at the
state of interest from table or chart.
• Method 2: define a reference state and set Ê = 0 at this state.
Find a model equation that describes how Ê depends on the
state relative to the reference state.
Internal energy and enthalpy
Internal energy (U)
• Energy stored in molecules in the form of covalent chemical bonds,
noncovalent intermolecular forces, and thermal motion
• Exclude any system energy due to external forces such as system’s
velocity (kinetic energy) or its position (potential energy)
• A function of pressure (P), temperature (T), phase (), compositions (xi)
Enthalpy (H)
• total energy of a thermodynamic system
• internal energy + energy required to make room for the system by
establishing its volume and pressure
• Û and Ĥ are defined relative to some reference state (state of matter)
• State of matter is specified by pressure, temperature, phase, composition
Using tables and graphs to find Û and Ĥ
Steam table (table 6.1)
• Û and Ĥ as a function of P, T, 
• Reference state: P = 0.006116 bar, T = 0.01 °C,  = liquid, xw = 1
(triple point of water)
•
Û = 0 at reference state
Linear interpolation
• At values of T and P that are not shown on the table
• Use proportionality
Û and Ĥ of pure water
• Large increase in Û and Ĥ with a change in phase from liquid to vapor
• Û and Ĥ increase linearly with an increase of T at constant phase
• Û and Ĥ are nearly identical in the liquid phase at identical temperature
and pressure, but Ĥ is slightly greater than Û in the vapor phase
• Û and Ĥ are not strong functions of pressure at low pressure and in the
liquid phase
Example 6.5
No data at 60 °C → use linear interpolation
Example 6.7
Reference state: pure liquid
water at 273 K and pure liquid
ammonia at 196 K at 1 bar
1. Ĥ = 0 at reference state
2. Ĥ = -140 kJ/kg solution, 34 wt% ammonia
3. Ĥ = 200 kJ/kg solution
4. For water at 1 bar, 373 K, Ĥw = 405 kJ/kg
For saturated liquid ammonia at 1 bar, 80 wt%,
Ĥs = -260 kJ/kg
0.34
The mixture is 40 wt% ammonia
From the graph at 1 bar, 40 wt% → Ĥs = -200 kJ/kg
Using model equations to find Û and Ĥ
• When we don’t have tables or charts
• Use model equations to calculate the change in Û or Ĥ with a
change is one property (P, T, phase, composition), while
holding all other properties constant
Change in Û and Ĥ with change in P
• For ideal gases with change of P1 to P2 at constant T, , xi
Still good approximation for real gases at small pressure change
• For solids and liquids,
Change in Û and Ĥ with change in T
• The change in Ĥ is proportional to the change in T at constant P, , xi
• proportionality constant → constant pressure heat capacity (Cp)
• If Cp is independent of temperature at constant P, , xi
• The change in Û is proportional to the change in T at constant volume, , xi
• proportionality constant → constant volume heat capacity (Cv)
• If Cv is independent of temperature at constant V, , xi
• For gases undergoing large temperature changes,
Cp and Cv are functions of temperature
• Polynomial expressions for Cp of some compounds in App. B
• Relationships between Cp and Cv
for liquids and solids
for gases
Change in Û and Ĥ with change in 
• Enthalpy of vaporization (Ĥv) for liquid (state 1) to vapor (state 2)
• Enthalpy of melting ( Ĥm) for solid (state 1) to liquid (state 2)
• Enthalpy of condensation (vapor to liquid) and of fusion (liquid to solid)
are the negative of vaporization and melting enthalpies
• Relationships between enthalpy and internal energy of phase changes
Change in Û and Ĥ with change in xi : Mixing and solution
• Enthalpy of mixing (Ĥmix): composition change only
✓ Ĥmix  0 for mixing vapors, gases, and liquids with similar
chemical components
✓ Ĥmix  0 for mixing if there are strong noncovalent attractive
or repulsive interactions between two components
• Enthalpy of solution (Ĥsoln): both composition and phase change
✓ Enthalpy of crystallization is negative of Ĥsoln
Change in Û and Ĥ with change in xi : chemical reaction
• Standard enthalpy of reaction (Ĥ°r): enthalpy change for a
chemical reaction at 298 K and 1 atm
Method 1
• standard enthalpy of formation (Ĥ°f,i): the enthalpy change for the
formation of one mole of compound i at 25 °C and 1 atm from its
elements in their natural phase and state of aggregation
Method 2
reference state, Ĥ°c,i = 0
• standard enthalpy of combustion (Ĥ°c,i): the enthalpy change for the
reaction of oxygen with compound i at 25 °C and 1 atm to generate
specific products of reaction; CO2 (g), H2O (g), SO2 (g), N2 (g), and Cl2 (g)
• Only for reactions involving molecular species containing olny C, H, O, N,
S and Cl
Enthalpy of vaporization
• Ĥ°f,i and Ĥ°c,i are functions of the phase of compound i.
• If Ĥ°f,i or Ĥ°c,i data for two different phases are given, the difference is the
Ĥ of phase change at 298 K
Change in internal energy for chemical reactions
• For liquid or solid phase, the change in pressure and volume
with chemical reaction is small
• For an ideal gas
T is constant because we are considering the change in
enthalpy due only to reaction
Change in Û and Ĥ with change in P, T, and 
• Û and Ĥ are state functions → not functions of the path of
the system got to that state
Example 6.8
Construct a pathway with the change of only one parameter
For solids and liquids
H  0 for small P for real gas
179.9 oC
Change in Û and Ĥ with change in P, T, , and xi
• The basis for the calculation of Û and Ĥ are different
✓ Enthalpy change for a reaction: per mole of
reaction
✓ Enthalpy change for temperature change of
reactants: per mole of reactant
✓ Enthalpy change for a dissolution: per mole
of solute
✓ Enthalpy change for temperature change of
solution: per mole of solution
With a change in chemical composition,
calculate U and H rather than Û and Ĥ
Example 6.9
Construct a pathway
From App. B
summary