Lecture 1-Principles of Thermodynamics.ppt

Chemical Engineering Department | University of Jordan | Amman 11942, Jordan

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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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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.



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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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Apply to an ideal gas with constant heat capacities undergoing a mechanically reversible

adiabatic process


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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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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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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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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.



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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.



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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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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

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Lecture 1-Principles of Thermodynamics.ppt