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Dr.-Eng. Zayed Al-Hamamre
Advance chemical Engineering Thermodynamics
Principles of Thermodynamics
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Content
The first law of thermodynamics
The General Energy Balance for A System
Energy Transfer by Work
Phase diagram
Properties Tables and Equations of States
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The first law of thermodynamics (the conservation of energy principle)provides a sound basis for studying the relationships among the various forms of energy and energy interactions.
The first law states that energy can be neither created nor destroyed during a process; it can only change forms.
The First Law: For all adiabatic processes between two specified states of a closed system, the net work done is the same regardless of the nature of the closed system and the details of the process.
o The net work must depend on the end states of the system only, represented by the
total energy (E).
o The change in the total energy during an adiabatic process must be equal to the
net work done.
The First Law of Thermodynamics
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The net change (increase or decrease) in the total energy of the system during aprocess is equal to the difference between the total energy entering and the totalenergy leaving the system during that process.
Energy balance
Energy is a property
Where
u1 and u2 can be determined directly from the property
tables or thermodynamic property relations
Energy Balance
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The General Energy Balance for A System
Energy balance for any system
undergoing any process
Energy balance in the rate form
For constant rate, the total quantities are related to the quantities per unit time is
Energy balance per unit mass basis
Energy balance in differential form
Energy balance for a cycle
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Change in amount of
energy contained within
the system during some
time interval
=
Net amount of energy
transferred in across the system
boundary by heat transfer
during the time interval
-
Net amount of energy
transferred out across the
system boundary by work
during the time interval
Energy Balance: Closed Systems
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Energy Balance: Closed Systems
dE Q W Differential Form:
Time Rate Form:dE
Q Wdt
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Energy balance when sign convention is used (i.e., heat input and work output are positive;
heat output and work input are negative).
Various forms of the first-law relation for
closed systems when sign convention is
used.
For a cycle E = 0, thus Q = W.
The first law cannot be proven mathematically, but no process in nature is known to have violated
the first law, and this should be taken as sufficient proof.
The General Energy Balance for A System
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Energy balance for a constant-pressure expansion or compression process
HWU b
For a constant-pressure expansion or
compression process:
An example of constant-pressure process
General analysis for a closed system
undergoing a quasi-equilibrium constant-
pressure process. Q is to the system and W is
from the system.
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Constant-Volume and Constant-Pressure Processes
Remember that in the liquid-vapor saturation region,
and
b
If Wothre = 0.0, then
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Constant-Volume and Constant-Pressure Processes
Since
Since for closed systems, n is also constant
zero
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Formal definitions of cv and cp.
Three Ways of Calculating u and h
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Specific Heat Relations of Ideal Gases
The cp of an ideal gas can be determined
from a knowledge of cv and R.
On a molar basis
The relationship between cp, cv and R
Specific heat ratio
The specific ratio varies with temperature,
but this variation is very mild.
For monatomic gases (helium, argon, etc.),
its value is essentially constant at 1.667.
Many diatomic gases, including air, have a
specific heat ratio of about 1.4 at room
temperature.
dh = cpdT and du = cvdT
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Equations for Process Calculations: Ideal Gases
Since
For an ideal gas in any mechanically reversible closed-system process
(if Wother = 0.0)
( )
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Equations for Process Calculations: Ideal Gases
But
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Isothermal Process
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Isobaric Process
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lsochoric (Constant- V) Process
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Adiabatic Process: Constant Heat Capacities
An adiabatic process is one for which there is no heat transfer between the system and its
surroundings
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Adiabatic Process: Constant Heat Capacities
Apply to an ideal gas with constant heat capacities undergoing a mechanically reversible
adiabatic process
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Adiabatic Process: Constant Heat Capacities
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Polytropic Process: Constant Heat Capacities
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Polytropic Process
Isobaric process (constant pressure process): δ = 0.
Isothermal process:, δ = 1.
Adiabatic process: δ = γ.
Isochoric process: dV/dP = V/Pδ; for constant V, δ =
Paths of polytropic processes
characterized by specific values
of δ
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Enthalpy Changes
The enthalpy of a compressed liquid
A more accurate relation than
U, H and Specific Heat of Solids and Liquids
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Energy Transfer by Work
Heat and work are directional quantities, and thus the complete description of a heat or
work interaction requires the specification of both the magnitude and direction
Work is also Path functions have inexact differentials,
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Energy Transfer by Work
Expansion or Compression Work
As the gas expands its pressure exerts a
normal force on the piston.
p denote the pressure acting at the interface
between the gas and the piston., A is the area
of the piston face.
The force exerted by the gas on the piston is
simply the product pA,
The work done by the system as he piston is
displaced a distance dx is
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Energy Transfer by Work
For simple compressible substances
in reversible processes, the work
done can be represented as the area
under a curve in a pressure-volume
diagram
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Moving Boundary Work
Moving boundary work (P dV work): The
expansion and compression work in a piston-
cylinder device.
The work associated with
a moving boundary is
called boundary work.
A gas does a differential
amount of work Wb as it
forces the piston to move
by a differential amount ds.
Quasi-equilibrium process: A process
during which the system remains nearly
in equilibrium at all times.
Wb is positive for expansion
Wb is negative for compression
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The area under the process
curve on a P-V diagram
represents the boundary
work.
The boundary work done during
a process depends on the path
followed as well as the end
states.
The net work done during a
cycle is the difference between
the work done by the system
and the work done on the
system.
Moving Boundary Work
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Polytropic, Isothermal, and Isobaric processes
Polytropic process: C, n (polytropic exponent) constants
Polytropic process
Polytropic and for ideal gas
When n = 1 (isothermal process)
Schematic and P-V diagram
for a polytropic process.
Constant pressure process
What is the boundary work for a
constant-volume process?
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Saturated vapor: A vapor that is about to condense.Saturated liquid–vapor mixture: The state at which the liquid and vapor phases coexist in equilibrium.Superheated vapor: A vapor that is not about to condense (i.e., not a saturated vapor).
As more heat is transferred, part of the saturated liquid vaporizes (saturated liquid–vapor mixture).
At 1 atm pressure, the temperature remains constant at 100°C until the last drop of liquid is vaporized (saturated vapor).
As more heat is transferred, the temperature of the vapor starts to rise (superheated vapor).
Phases Change Processes of Pure Substance
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T-v diagram for the heating process of
water at constant pressure.
If the entire process between state 1 and 5 described in the figure is reversed by cooling the water while maintaining the pressure at the same value, the water will go back to state 1, retracing the same path
The amount of heat released will exactly match the amount of heat added during the heating process.
Phases Change Processes of Pure Substance
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Saturation Temperature and Saturation Pressure The temperature at which water starts boiling depends on the pressure; therefore, if
the pressure is fixed, so is the boiling temperature.
Water boils at 100C at 1 atm pressure.
Saturation temperature Tsat: The temperature at which a pure substance changes phase at a given pressure.
Saturation pressure Psat: The pressure at which a pure substance changes phase at a given temperature.
The liquid–vapor saturation
curve of a pure substance
(numerical values are for
water).
Control the boiling temperature of
a substance by simply controlling
the pressure,
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Phase Diagramscondensation at constant TVaporization at
constant T
sublime
TO-TN: Degrees of superheat
TN is Tsaturated
Vapor at T > Tsaturated at
a given P, or
Vapor at P < Psaturated at
a given T.
Vapor at T < Tsaturated
at a given P, or
Vapor at P > Psaturated
at a given T.
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Latent heat: The amount of energy absorbed or released during a phase-change process.
Latent heat of fusion: The amount of energy absorbed during melting. It is equivalent to the amount of energy released during freezing.
Latent heat of vaporization: The amount of energy absorbed during vaporization and it is equivalent to the energy released during condensation.
The magnitudes of the latent heats depend on the temperature or pressure at which the phase change occurs.
At 1 atm pressure, the latent heat of fusion of water is 333.7 kJ/kg and the latent heat of vaporization is 2256.5 kJ/kg.
The atmospheric pressure, and thus the boiling temperature of water, decreases with elevation.
Phases Change Processes of Pure Substance
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A liquid cannot vaporize unless it absorbs energy in the amount of the latent heat of
vaporization,
The rate of vaporization of a fluid depends on the rate of heat transfer to it.
The rate of heat transfer to the fluid and thus the rate of vaporization can be minimized by
insulating the container heavily.
During phase change, both T and P remain constant.
Some Consequences of Tsat and Psat Dependence
A relatively simple empirical equation that correlates vapor pressure-temperature data
extremely well is the Antoine equation.
A, B and C are constants
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The State Principle
Two independent, intensive, thermodynamic properties are required to fix the state of a simple compressible system (systems of commonly encountered pure substances, such as water or a uniform mixture of non-reacting gases in the absence of motion, gravity, and surface, magnetic, or electrical effects).
For example: P and v
T and u
x and hIntensive thermodynamic properties:
h – specific enthalpy
u – specific internal energy
x – quality
(steam only)
s –specific entropy
P –absolute pressure
T – absolute temperature
v – specific volume
Less used:
g - Gibbs free energy
a - Helmholz free energy
The functional relations would be developed using experimental data and would depend
explicitly on the particular chemical identity of the substances making up the system
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A substance may be approximated as a simple compressible substance if effects due to other reversible
work modes are negligible.
Substances whose surface effects, magnetic effects, and electrical effects are insignificant when dealing
with the substances. But changes in volume, such as those associated with-the-expansion of a gas in a
cylinder, are very important.
i.e. the only mode of energy transfer by work that can occur as a simple compressible system
undergoes quasiequilibrium processes, is associated with volume change and is given by
For example,
o If the surface-to-volume ratio of a large body of water is small enough, then surface tension will not
measurably affect the properties of the water except very near the surface.
o On the other hand, surface tension will have a dramatic influence on the properties of a very small
water droplet.
i.e. a very small water droplet can't be treated accurately as a simple compressible substance, while a
large body of water is approximated very well in this way.
A simple compressible substance may exist in different phases: solid, liquid, or gas. Some substances
have multiple solid phases, some even have multiple liquid phases (helium), but all have only one gas
phase.
Simple Compressible Substance
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At pressures above the critical pressure,
There is not a distinct phase change process
The specific volume of the substance continually increases, and
at all times there is only one phase present
Above the critical state, there is no line that separates the
compressed liquid region and the superheated vapor region.
The saturated liquid states can be connected
by a line called the saturated liquid line,
and saturated vapor states in the same figure
can be connected by another line, called the
saturated vapor line
Or wet region
(boiling)
T-V diagrams
Constant pressure lines
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P-V diagrams
P-v diagram of a pure substance.The pressure in a piston–
cylinder device can be reduced
by reducing the weight of the
piston.
Constant
temperature lines
Or wet region
(boiling)
V increase at constant P
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Property Tabls For most substances, the relationships among thermodynamic properties are too complex to be
expressed by simple equations.
Therefore, properties are frequently presented in the form of tables.
Some thermodynamic properties can be measured easily, but others cannot and are calculated by using the relations between them and measurable properties.
The results of these measurements and calculations are presented in tables in a convenient format.
A separate table is prepared for each region of interest such as the superheated vapor, compressed liquid, and saturated (mixture regions).
Enthalpy—A Combination Property
The combination u + P*v is
frequently encountered in the
analysis of control volumes.
The product pressure volume has energy units.
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Saturated Liquid–Vapor Mixture
Quality, x : The ratio of the mass of vapor to the total mass of
the mixture. Quality is between 0 and 1 0: sat. liquid,
1: sat. vapor.
The properties of the saturated liquid are the same whether it exists alone or in a mixture with saturated vapor.
The relative amounts of liquid and vapor phases in a
saturated mixture are specified by the quality x.
(1-x) gives Moisture Content
Temperature and pressure
are dependent properties
for a mixture.
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Examples: Saturated liquid-vapor mixture states on T-v and P-v diagrams.
Saturated Liquid–Vapor Mixture
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Quality Relations
LET b = ANY INTENSIVE PROPERTY– (b = v, u, h, s, etc.)
(1 )
f f
g f fg
f fg
fg g f
g f
b b b bx
b b b
b b x b
b b b
b x b x b
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Superheated Vapor In the region to the right of the saturated
vapor line and at temperatures above the
critical point temperature, a substance
exists as superheated vapor.
In this region, temperature and pressure
are independent properties.
A partial listing
of Table A–6.
At a specified P, superheated
vapor exists at a higher h than the
saturated vapor.
Compared to saturated vapor, superheated
vapor is characterized by
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Compressed LiquidCompressed liquid is characterized by
y v, u, or h
A more accurate relation for h
A compressed liquid may
be approximated as a
saturated liquid at the
given temperature.
The compressed liquid properties
depend on temperature much more
strongly than they do on pressure.
At a given P and T, a pure
substance will exist as a
compressed liquid if
75oC
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The Ideal Gas Equation of State Equation of state: Any equation that relates the pressure, temperature, and
specific volume of a substance.
The simplest and best-known equation of state for substances in the gas phase is the ideal-gas equation of state. This equation predicts the P-v-T behavior of a gas quite accurately within some properly selected region.
R: gas constant
M: molar mass (kg/kmol)
Ru: universal gas constant
Ideal gas equation of state
Different substances have
different gas constants.
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Compressibility Factor Z
The compressibility factor is unity for
ideal gases.
Compressibility factor Z: A
factor that accounts for the
deviation of real gases from ideal-
gas behavior at a given
temperature and pressure.
The farther away Z is from unity, the more the gas
deviates from ideal-gas behavior.
Gases behave as an ideal gas at low densities (i.e., low pressure, high temperature).
Question: What is the criteria for low pressure
and high temperature?
Answer: The pressure or temperature of a gas is
high or low relative to its critical temperature or
pressure.
At very low pressures, all gases approach ideal-
gas behavior (regardless of their temperature).
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49Comparison of Z factors for various gases.
Gases deviate from the ideal-gas
behavior the most in the neighborhood
of the critical point.
Pseudo-reduced specific volumeZ can also be determined from a
knowledge of PR and vR.
Compressibility Factor Z
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Other Equation of States
Several equations have been proposed to represent the P-v-T behavior of substances accurately over a larger region with no
limitations.
Van der Waals Equation of State
Critical isotherm of a pure substance
has an inflection point at the critical
state.
This model includes two effects not considered in
the ideal-gas model: the intermolecular attraction forces and the volume occupied by the molecules themselves. The accuracy of the van der Waals
equation of state is often inadequate.
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Beattie-Bridgeman Equation of StateThe constants are given in Table 3–4 for
various substances. It is known to be
reasonably accurate for densities up to
about 0.8cr.
Benedict-Webb-Rubin Equation of State
The constants are given in Table 3–4. This equation can handle substances at densities up to
about 2.5 cr.
Virial Equation of State
The coefficients a(T), b(T), c(T), and so on, that are functions of temperature alone are called
virial coefficients.
Other Equation of States
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Virial Equations of State
where B, C, and D are functions of temperature and are known as the
second, third, and fourth virial coefficients, respectively.
Since theoretical and experimental data is not readily available for
viral coefficients higher than the second one, the equation is often
used in truncated form.
And
in the gas region (single phase system)
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Where
(The reduced
temperature) ω: is Pitzer acentric factor,
a parameter that reflects
the geometry and polarity of
a molecule
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Virial Equations of State
where B, C, and D are functions of temperature and are known as the second, third, and fourth virial coefficients, respectively.
Since theoretical and experimental data is not readily available for viral coefficients higher than the second one, the equation is often used in truncated form.
And
in the gas region (single phase system)
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Where
(The reduced temperature)
ω: is Pitzer acentric factor, a parameter that reflects the geometry and polarity of a molecule
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Cubic Equations of State are PVT relationships when expanded, results in third-order equations for the specific volume
Van der Waals equation of state:
Where
Soave-Redlich-Kwong (SRK) equation:
Or
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Where
the b term is a volume correction, while the a is a molecular interaction parameter.
ω: is Pitzer acentric factor, a parameter that reflects the geometry and polarity of a molecule
Solving the cubic equation typically requires an iterative ("trial-and-error") solution.
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Constants for the Van der Waals and Redlich-Kwong 'Equations Calculated From the Listed Values of the Critical Constants
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Equation of States