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7/28/2019 Energy Balance for Nonreactive Processes-p1
1/12
ENERGY BALANCE FOR
NONREACTIVE PROCESSESpart 1
4.1 Elements of energy balance equationsa. Reference states
b. Hypothetical process paths
c. Procedure for energy balance calculations
4.2 Changes in pressure at constant temperature
4.3 Changes in temperaturea. Sensible heat and heat capacities
b. Heat capacity formulas
c. Estimation of heat capacities
d. Energy balance on single phase systems
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4.1 Elements of energy balance equations
A common practice is to arbitrarily designate a reference
state for a substance at which U or H is declared to equalzero.
Then tabulate U and/or H for the substance relative tothe reference state.
Referencestate
U and H are state properties of a species; their values
depend only on the state of the species primarily on its temperature
and state of aggregation (solid, liquid or gas)
and, to a lesser extent, on its pressure (and formixtures of some species, on its mole fraction in themixture).
Stateproperties
Construct a hypothetical process path from the initialstate to the final state consisting of a series of steps.
When a species passes from one state to another, both
U and H for the process are independent of the pathtaken from the first state to second one
Process path
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Example
Compressing H2 gasfrom 1 atm to 300
atm at 25oC
Changes in P at constantT and state ofaggregation
Melting ice at 0oC
and then heatingthe liquid water to
30oC all
Phase changes atconstant T and P-
melting, solidifying,vaporizing,condensing,
sublimating
Changes in T at constantP and state ofaggregation
Mixing sulfuric acidand water at aconstant
temperature of20oC and a constant
pressure 1 atm
Mixing of two liquids ordissolving of a gas or a
solid in a liquid atconstant T and P
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c. Procedure for energy balance
calculations
Perform all requiredmaterial balance
calculations
Write appropriateform of the energybalance (closed or
open system)
Choose a referencestate-phase, T, P- foreach of the species
involved in theprocess
For a closed constantvolume system,
construct a table withcolumns for initial andfinal amounts of eachspecies and specific
internal energiesrelative to the chosenreference state.
For an open system,construct a table withcolumns for inlet and
outlet streamcomponent flow rates
and specific enthalpies
relative to the chosenreference state.
Calculate all requiredvalues of Ui or Hi and
insert values in theappropriate places in
the table
Calculate Q foropen or close
system
Calculate any work, kinetic energy, orpotential energy terms that you have
not drop from the energy balance
Solve the energy balance
for whichever 4
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4.2 Changes in pressure at constant
temperature
If the pressure of a solid or liquid changes atconstant T,
U = 0
H = [U + (PV)] = [U + PV + VP] = [VP]
Both U and H independent of pressure for ideal
gases
may assume
U = 0 and
H = 0 for a gasundergoing an isothermal pressure change unless gas temperature below 0 0C or
well above 1 atm are involved.
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4.3 Changes in temperature
a. Sensible heat and heat capacities
The term sensible heat signifies that heat must be transferred to raise orlower the temperature of a substance or mixture of substances.
The quantity of heat required to produce a temperature change:
Q = U (closed system)
Q = H (open system)
Heat capacity at constant volume Cv. At constant volume:
6
dTTCUT
T
v
^
2
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Suppose both temperature and the volume
of a substance change. To calculate Ubreak the process into 2 steps ( a change inVat constant Tfollowed by a changes in T
and constant V):
7
21
222111
21
^^^
UU
UUU
V,TAV,TAV,TA^^
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For ideal gas and (to a goodapproximation) liquid and
solids, U depends only on T. Instep 1, Tis constant, U1 = 0.
Step 2 Vis constant:
8
dTTCUT
T
v2
1
^
Ideal gas: Exact
Solid or liquid: good approximation
Non ideal gas: valid only ifVis
constant
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Heat capacity at constant pressure Cp. At
constant pressure:
For first step refer section 8.2 (Felder), as Tis
constant,
H1 = 0 (for ideal gas),
H1 = V
P(for solid or liquid).
Step 2 P is constant:
9
dTTCHT
T
p 2
1
^
dTTCPVHT
T
p2
1
^^
dTTCHT
T
p2
1
^
Solid or liquid Ideal gas: ExactNon ideal gas: valid only if P
is constant
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b. Heat capacity formula
Heat capacities are functions oftemperature and frequently
expressed in polynomial form(Cp = a + bT + cT
2 + dT3).
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constantGas:R
RCC:GasesIdeal
CC:SolidsandLiquid
vp
vp
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c. Estimation of heat capacity
Kopps rule
simple empiricalmethod for
estimating the
heat capacity of asolid or liquid near
200C.
For heat capacitiesof certain mixture may use these
rules:
Rules 1 : For a mixture of gases
or liquids, calculate the totalenthalpy change as the sum ofthe enthalpy changes for the
pure mixture component
Rules 2 : For a highly dilutesolutions of solids or gases inliquids, neglect the enthalpy
change of solute.
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For heat capacities of certain mixture: (Cp)mix (T)
For enthalpy calculation:
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componentiofcapacityheatCcomponentioffractionmoleormassy
mixtureofcapacityheatC
where
TCyTC
pi
i
mixp
componentsmixture
allpiimixp
2
1
TCmixp
^T
T
dTH