energy balance for nonreactive processes-p1

7/28/2019 Energy Balance for Nonreactive Processes-p1

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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


10/12

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:

12

componentiofcapacityheatCcomponentioffractionmoleormassy

mixtureofcapacityheatC

where

TCyTC

pi

i

mixp

componentsmixture

allpiimixp

2

1

TCmixp

^T

T

dTH

energy balance for nonreactive processes-p1

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