8 nonreactive process balances

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Balances on

Nonreactive ProcessesCh E 201Material and Energy Balances



State Property CalculationsCal

cul

atio

n o

f



Hypothetical Process PathsSin

ce

stat

e p

r



Hypothetical Process Paths



Energy Balance CalculationProcedure

. Per

f or

m al

l r

e




. Con

str

uct

a t

a




. Cal

cul

ate:

– open




. Cal

cul

ate

any



Condenser Energy BalancePar

tia

l co

nde

n

0 0 0



Condenser Energy Balance. C

ho

ose

ref

ere

n




on

str

uct

inl

e




al

cul

ate

unk

n



Condenser Energy Balanceyp

oth

etic

al

p




oth

etic

al

p



Condenser Energy Balance

h

ang

e in




oth

etic

al

p




oth

etic

al

p

C




al

cul

ate

unk

n

35.7

1.16

32.0

-0.10

C




al

cul

ate

35.7

1.16

32.0

-0.10

C




al

cul

ate

non

z

I



Changes in P at Constant TIt has been

obs

e

S



Changes in T at constant PSen

sib

le h

eat

T



Changes in T at constant P The

sl

ope

of

t



Changes in T at constant P

• exact for an ideal gas• good approximation for a solid or

liquid• valid for nonideal gas only if V is

constant

C



Changes in T at constant PCal

cul

ate

Q r

e

C



Changes in T at constant PCon

sider t

he

e

i



Hypothetical Pathini

tial st

ate

H



Heat Capacity FormulasHea

t capac

ity

A



Cooling of an Ideal GasAss

uming i

dea

l

N



Cooling of an Ideal Gas. N

2

f lowing

at



Cooling of an Ideal Gas2. N2 in 5 L flask initially 3 bar, cooled

from 90 to 30°C – get CP for N2 from Table B.2, subtract R

to get CV

– calculate internal energy change

K



Estimate Heat Capacity of a PureSubstance

K op

p’s Rul

e i

s

E ti t H t C iti fR



Estimate Heat Capacities of Mixtures

Rul

e 1 – F

or

a

Energ Balance SingleF



Energy Balance: Single-Phase System

For

heatin

g/c

o

Energy Balance Gas



Energy Balance: GasPreheater

Ass

ume

ide

a

0 0 0

Energy Balance Gas




Energy Balance: Gas




• ideal gas neglect effect of P on H→

• neglect heat of mixing of gas phasecomponents

Energy Balance: Gas




• ideal gas neglect effect of P on H→

• neglect heat of mixing of gas phasecomponents

•

from Table B.8:

12.09

Energy Balance: Gas




12.09

8.17-0.15

Energy Balance: Waste Heat



Energy Balance: Waste HeatBoiler

Energy Balance: Waste Heat



Energy Balance: Waste HeatBoiler

T



Latent Heats The

specif

ic

e

A



Heat of VaporizationAt

what ra

te

(

O



Heat of VaporizationOf t

en a ph

ase



Heating and Vaporization

0 0 0




true path

but don’t knowvap(146°ΔĤ

C) at step E




shortest path

don’t knowvap(25°C)ΔĤ

at step C




hypothetical path

permits use of knownvap(69°C)ΔĤ

at step D




TableB.1

TableB.2




TableB.1




TableB.2




note contribution of term to total of ΔĤpath

Estimation/Correlation of LatentH



Estimation/Correlation of LatentHeats

Hea

t of va

por

i

Estimation/Correlation of LatentW



Estimation/Correlation of LatentHeats

Wat

son’s C

orr

e

Energy Balance: System w/ PhaseA



Energy Balance: System w/ PhaseChange

An

equimol

ar

m

Energy Balance: System w/ Phase




total molebalance:benzenebalance:





5.332

6.34

037.52

42.93

P h i ChA



Psychrometric Charts p

s y chr om

et r

i



Psychrometric chart – SI Units.Reference states:H2O (L, 0°C, 1 atm), dry air (0°C,1 atm).



Dry Bulb Temperature:air temperature asmeasuredby a thermometer.



absolute humidity, ha:moisture content,measuredin kg H2O/kg DA

easily converted to mass fraction:e.g., if ha = 0.0150 kg H2O/kg DA,then mH2O = 0.0150 kg H2O/(1.015 kghumid air)

= 0.0148 kg H2O/kg



relative humidity, hr hr =[pH2O/p*H2O(T)]×100%



Dew Point (saturation temp),Tdp:found by moving horizontallyfroma given air hr and temperature

e.g., air at 29°C, 20% relativehumidity

has a dew point of 4°C



e.g., volume of 1 kg humid air (HA) 30°C,30% hr:

humid volume



wet bulb temperature,Twbis the lowest temperature an object may becooled to by the process of evaporation. Waterevaporating from a moistened wick on the wet-

bulb thermometer bulb cools the thermometerbulb and lowers the temperature reading. Thecooling effect of the evaporation from the bulb isinversely proportional to the amount of watervapor present in the air: the more water vaporpresent, the less moisture will evaporate from themoistened wick, and the less cooling of thethermometer bulb will occur.

From the dry- and wet-bulb readings, the dew-point temperature and humidity values may becalculated.

specific enthalpy of saturated air, Ĥ



Represents enthalpy change of dry airand accompanying water vapor.

Can be obtained by adding the sensibleheat of DA from reference state (0°C)to 25°C,with H2O = H2O(v, 25°C) - H2OΔĤ Ĥ Ĥ(l, 0°C)

enthalpy devation



used to determine enthalpyof air that is not saturated

e.g., 35°C 10% rel. hum air=ΔĤ 45.0 – 0.52 = 44.45kJ/kg DA

Using the Psychrometric



Using the PsychrometricChart

Estimate the absolute

humidity, wet-bulbtemperature, humidvolume, dew point, andspecific enthalpy of humidair at 41°C, 10% relative

humidity.

3°C

19°C 0.895

m3/kg

0 . 0

0 4 8

k g

H 2 O / k g

D A

54.2 – 0.7 = 53.5 kJ/kgDA

41°C

1 0 % r e l

.

h u m.

Air Conditioner



Air Conditioner•

DOF analysis7 unknowns (m1, m2, m3, 1, 2, 3, Q)Ĥ Ĥ Ĥ

- 1 material balance (DA already balancedon flowchart)

- 2 absolute humidities from psychrometriccharts (inlet/outlet)

- 2 enthalpies from psychrometric charts

(inlet/outlet)- 1 enthalpy of condenstate- 1 energy balance- 0 degrees of freedom

Air Conditioner



Air Conditioner

0.018 lbmH2O/lbm DA

0.0079 lbmH2O/lbm DA

waterbalance:

fractioncondensed:

Air Conditioner

condensate enthalpy( f t t i li id t t



Air Conditioner

1 = 38.8ĤBTU/lbm DA


(reference state is liquid water at32°F):





3 = 19.0ĤBTU/lbm H2O EnergyBalance

cooling requirement for





3 = 19.0ĤBTU/lbm H2O

cooling requirement for1000 ft3/min of delivered air

Adiabatic CoolingAd



Adiabatic Coolingdi

abatic

coo

l

Adiabatic CoolingIf



Adiabatic Coolingf

certain

, w

e

Adiabatic HumidificationA



Adiabatic Humidification s

tream o

f ai

Adiabatic HumidificationAs



Adiabatic Humidificationss

ume the

hea



0.0026 kg H2O/kgDA

13.2°C

0.0063 kg H2O/kg

DA21.2°C

ExitingAir

EnteringAir

evaporationrate:

8 nonreactive process balances

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