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CHAPTER 8 : BALANCES ON NONREACTIVE PROCESSES (8.3 CHANGES IN TEMPERATURE,…
CHAPTER 8 : BALANCES ON NONREACTIVE PROCESSES
8.1 ELEMENTS OF ENERGY BALANCE EQUATION
:check:Reference State:
H = U+ PV
:check:Closed
ΔU = ∑f n,Û - ∑i n,Û,
Q + W = ΔU + ΔΕk + ΔEp
:check:Open
ΔH = ∑out n,Ĥ - ∑in n,Ĥ,
Q+Ws = ΔH+ΔEk+ΔEp
Non reactive process : without chemical reaction, depends on physical / environment factor
DIFFERENT BETWEEN CLOSE AND OPEN
:check:CLOSE :
n (amount)
U (internal energy)
Û (specific internal e.)
:check:OPEN : ṅ (molar flow rate) Ḣ (rate of enthalpy) Ĥ (specific enthalpy)
8.2 CHANGES IN PRESSURE AT CONSTANT TEMPERATURE
:check:ΔÛ =ΔĤ = 0 (Ideal gas)
:check: ΔĤ =0 , ΔÛ = 0 (Real gas)
:check: ΔĤ=VΔP , Nearly independent of pressure (solids and liquids)
ΔT at constant P
Sensible heat must be transferred to RAISE or LOWER the temp. Q = ΔU (closed) ,Q = ΔH (open)
Ideal gas: exact Solid or liquid: good approximation nonideal gas: valid only if V is constant
8.3 CHANGES IN TEMPERATURE
sensible heat
Signifies that heat that must be transferred to raise pr lower the temperature of a substance or mixture of substances.
heat capacity
constant volume (Cv)
:ballot_box_with_check:dÛ = Cv(T)dT
constant pressure (Cp)
:ballot_box_with_check:dĤ= Cp(T)dT
heat capacity formulas
polynomial form: Cp= a+bT+cT^2 +dT^3
liquid & gases: Cp Cv
ideal gases: Cp=Cv+R
Gases:
Liquid and solids:
Kopp's Rule
a simple empirical method for estimating the heat capacity of solid or liquid at or near 20°C
:red_flag: Rule 1
for a mixture of gases or liquid, calculate total enthalpy changes for mixture component
:red_flag: Rule 2
for highly dilute solutions of solids or gases in liquids, neglect the enthalpy change of solute
numerical integration of tabulated heat capacities
Simpson's Rule
8.4 PHASE-CHANGE OPERATION
latent heats
changes in specific enthalphy associated with specific T and P
phase changes
heat of melting
heat of fusion
estimation and correlation of latent heat
Trouton's rule
Approximation of standard heat of fusion
Clausius-Clayperon
Watson's correlation
Chen's equation
energy balance on process involving phase change
liquid(reference state),vapor(process stream):
bring liquid from reference temp.at which ΔĤv is known
vaporize the liquid
bring vapor to the process stream temp.
sum the individual enthalphy changes for the three steps
Value listed in Psychometric chart
dry bulb temp.
temp. measured by common temp. measurements instuments
absolute humidity
mass ratio of water vapor to dry air
relative humidity
humid volume
volume per mass of dry air
wet bulb temp.
entalphy per mass of dry air
Adiabatic cooling
warm gas----cold liquid-----gas cooling-----liquid evaporated
heat transferred from gas to liquid
(but Q=0)
common process
spray dehumidification
drying
spray cooling, spray humidification
spray drying
8.5 MIXING AND SOLUTION
balances on dissolution and mixing process
1)
calculate its enthalphy at 25°C
2)
add the enthalphy for the heating or cooling of the solution
3)
enthalphy from 2nd step should be calculated from tabulated solution heat capacities
:warning: use average heat capacity determined using equation (8.3-13)
enthalpy concentration chart
a plot of spesific enthalphy vs mole fraction
reference condition:
:check: pure liquid H2SO4 at 77°F
:check: liquid water at 32°F
heat of solution and mixing
an enthalphy change associated with mixing process of certain liquids and the dissolving of some gases or solids in a liquid solvent at given temperature and pressure
