Quantification of Macroscopic Property Theory Vs Practice

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Quantification of Macroscopic PropertyTheory Vs
Practice

• P M V Subbarao
• Professor
• Mechanical Engineering Department
• I I T Delhi

An Effort to Develop Some Understanding about
System
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Definition of A Thermodynamic Property

• Any Macroscopic variable, which can be written as
  a point function can be used as a thermodynamic
  property
• Thermodynamic properties are so related that F(.)
  is constant.
• Every substance is represented as F(.) in
  Mathematical (Caratheodory) Thermodynamics.
• This is shows a surface connectivity of Property
  of a substance.

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Mathematical description of A Substance
Identification of Phase of A Substance
ß 10-3/K for liquids ß 10-5/K for solids
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p-v-T Diagram of H2O
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Global Change in any Selected Property Type I
Given a path pf(T), to evaluate
From A to B.
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Global Change in any Selected Property Type II
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Corollaries on Properties.

• Corollary 1 A change of state is fully described
  by means of the initial and final values of all
  the primitive properties of the system.
• A change occurs when at least one of its
  primitive properties changes value.
• Corollary 2 A process is required for the
  determination of a derived property.
• Corollary 3 The change in value of a property
  is fixed by the end states of a system undergoing
  a change of state and is independent of the path.
• Corollary 4 Any quantity which is fixed by the
  end states of a process is a property.
• Corollary 5 When a system goes through a cycle,
  the change in value of any property is zero.
• Corollary 6 Any quantity whose change in a cycle
  is zero is a property of a system.

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The Nature of Macroscopic Property

• A pseudo description, but highly practicable.
• Suitable analytical and experimental methods will
  help in identifying change in a macroscopic
  property.
• It is possible to enhance the precision of Change
  detection/identification.
• Difficult to quantify this change with a number
  (integer or Real).
• What is a unit of a macroscopic property?
• How to get zero value of macroscopic property.

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The Most Important (Macroscopic)Thermodynamic
Property

• The most interesting macroscopic property in
  thermodynamics is Temperature.
• Pressure is equally important.
• Precise identification of change in temperature
  or change I pressure was done very early.
• Special instruments to identify the change in
  temperature were invented well before 16th
  century.
• These were called Thermoscope

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Thermoscope

• An instrument to measure heat and cold was
  invented by Galileo during his stay in Padua.
• this thermoscope was designed by Galileo in 1597.
  
• The thermoscope consists of an egg-sized glass
  with a long neck.
• The jar is heated with the hands and partially
  immersed, upside down, in a container filled with
  water.

• When the hands are removed, the water rises in
  the neck.
• The experiment demonstrated the changes in air
  density caused by temperature variations.
• Santorio had built a similar instrument in Venice
  in 1612.

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Galileo Thermoscope

• A thermoscope could show the differences in
  temperature, allowing observers to know if
  something was getting hotter or colder.
• The thermoscope could not provide an exact
  temperature in degrees.
• In 1612, the Italian inventor Santorio Santorio
  added a numerical scale on his thermoscope and it
  was used to take human temperature

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Length Scale Thermoscope

• Ferdinand II, the Grand Duke of Tuscany, followed
  in 1654, inventing the first enclosed
  thermometer, using alcohol as a liquid.
• But it still lacked a standardized scale and was
  not very accurate.
• Olaus Roemer, a Danish astronomer, developed an
  alcohol-based thermometer using wine.
• He marked two points on his thermometer 60 to
  mark the temperature of boiling water and 7.5 as
  the point where ice melted.

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Newtons Hot Iron Thermometer

• In 17th century accepted thermal expansion of
  alcohol as a principle of thermometry.
• These conventional thermometers were used almost
  exclusively for meteorological or medical
  purposes.
• NEWTON was the first, to develop thermometers
  capable of investigating a wide range of thermal
  phenomena in the laboratory.
• Newton resorted to a stratagem which has always
  been considered to be ingenious.
• Newton Invented law of cooling in late 17th
  century, and conducted the first experiments on
  the nature of cooling.
• Newton applied this principle to develop an
  industrial thermometer with high range.

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A plausible 'wind tunnel' for Newton's
coolingexperiments.
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Newtons Law for High Temperature Thermometry

• If the excess of the temperature of the body
  above its surroundings is observed at equal
  intervals of time, the observed values will form
  a geometrical progression with a common ratio.
• The several degrees of heat were discovered.

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Newtons Temperature Scale

• Melting Snow 0 ?N
• Heat of Summer 4, 5 6 ?N
• Incubated egg body heat 12 ?N
• Water begins to boil 33? N
• Solidification of 50-50 tin bismuth liquid
  alloy 49 ?N
• Solidification of liquid lead 96 ?N
• Red hot Iron 192 ?N

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Gabriel Fahrenheit

• In 1709, he improved the Olaus alcohol
  thermometer, but found that mercury gave better
  results.
• This was followed by his invention of the mercury
  thermometer in 1714.
• Fahrenheit wanted to construct a scale in order
  to actually measure and record temperatures.
• At the time, the coldest temperature obtainable
  in the laboratory derived from a mixture of
  water, ice and ammonium chloride (sal ammoniac).
• As a reliable measure at the high end of the
  temperature scale, he selected 96 degrees as the
  temperature of the blood of a healthy man.
• Defining the coldest obtainable temperature as 0
  degrees.

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The Temperature Scale

• Fahrenheit got his two fixed points on his
  scale.
• This enabled him to specify the temperature at
  which water freezes as 32 degrees.
• The mercury thermometers could measure higher
  temperatures than was possible with alcohol.
• Fahrenheit adjusted his scale so that the high
  end was the boiling point of water which he
  defined, somewhat arbitrarily, as 212 degrees.
• With 180 degrees between the freezing and boiling
  points of water, normal body temperature was then
  adjusted to 98.6 degrees.

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TEMPERATURE

• Simply stated The degree of hotness or coldness
  of a substance, as measured on a thermometer.
• A measure of Average rms value of peculiar
  velocity of atoms/molecules of a system.
• Temperature Scale is quantify the Temperature.
• Fahrenheit
• oF (9/5 oC) 32
• Celsius or Centigrade
• oC 5/9 (oF - 32)
• Rankine
• R oF 459.67
• Kelvin
• K oC 273.15

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Properties of A Thermodynamic System

• A System should be described using a set of
  point functions.
• The change in these functions can be calculated
  without performing any action.
• Instruments can be easily developed to measure
  these functions.
• Function tables can be prepared and marketed.
• Any industrial process can use these tables.
• This function is called as PROPERTY in
  Thermodynamics.

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Temperature Scales Temperature Scales Temperature Scales Significance of Temperature
Fahrenheit Celsius Kelvin Significance of Temperature
9,944.45F 5,506.92C 5,780.07 K Black body temperature of visible surface of Sun
6,169.76F 3,409.87C 3,683.02 K Freezing point of tungsten
3,034.26F 1,667.92C 1,941.07 K Freezing point of titanium
1,984.32F 1,084.62C 1,357.77 K Standard freezing point of copper
1,947.53F 1,064.18C 1,337.33 K Standard freezing point of gold
1,763.20F 961.78C 1,234.93 K Standard freezing point of silver
1,220.58F 660.32C 933.47 K Standard freezing point of aluminum
787.15F 419.53C 692.68 K Standard freezing point of zinc
449.47F 231.93C 505.08 K Standard freezing point of tin
313.88F 156.60C 429.75 K Standard freezing point of indium
212F.00 100C.00 373.15 K Standard boiling point of water
136F.00 57.78C 330.93 K World record high air temperature
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98.60F 37C.00 310.15 K Human body temperature reference
85.58F 29.76C 302.91 K Standard melting point of gallium
68F.00 20C.00 293.15 K Room temperature reference
39.15F 3.97C 277.12 K Temperature of maximum water density
32.02F 0.01C 273.16 K Triple point of water
32F.00 0C.00 273.15 K Standard freezing point of water
0F.00 -17.78C 255.37 K Fahrenheit's zero
-37.90F -38.83C 234.32 K Triple point of mercury
-128.56F -89.20C 183.95 K World record low air temperature
-308.82F -189.34C 83.81 K Triple point of argon
-361.82F -218.79C 54.36 K Triple point of molecular oxygen
-415.47F -248.59C 24.56 K Triple point of neon
-434.82F -259.35C 13.80 K Triple point of molecular hydrogen
-459.67F -273.15C 0 K.00 Thermodynamic absolute zero
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A Simple Substance

• The simple substance f(T) K T.
• Thermometric substance.
• Any other simple property which varies with
  temperature is called the thermometric property.
• Ideal gas is a good thermometric substance.

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The relation between Pressure Temperature
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What is Temperature Really?

• Absolute Kelvin Temperature is proportional to
  average kinetic energy of atoms in a macroscopic
  system.

• When atoms collide they tend on the average, to
  equalize kinetic energy spreads equally over all
  atoms.
• This is called thermal equilibrium.

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Temperature Measuring Devices

• Liquid in glass
• Bimetallic
• Gas thermometers
• Thermocouple
• Resistance Temperature Detectors
• Radiation and optical pyrometers

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Liquid in Glass Thermometer
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Material Coefficient of Volumetric Thermal Expansion g in 10-6 /K
Mercury 180
Ethyl Alcohol 1120
petrol 950
Water 0 to 695 (4 to 90 0C)
Glass 9.9
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Bimetallic Expansion Thermometer
A Measure of Temperature
Material a in 10-6 /K
Chromium 4.9
Copper 16.5
lead 28.9
Zinc 30.2
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Thermocouple
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Standard Thermocouples

• The ASTM identifies eight standard types of
  thermocouples.

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Thermocouple temperature vs.Voltage graph
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Resistance Temperature Device
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Radiation Pyrometer
A radiation thermometer is an instrument which
collects radiation from a target and produces an
output signal, usually electrical, related to the
radiance, which is used to infer the temperature
of the target.
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Total Radiation Stefan-Boltzmann Law

• The maximum emissive power at a given temperature
  is the black body emissive power (Eb).
• Integrating this over all wavelengths gives Eb.

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The Problem of Quantification of Temperature

• Numerical description of temperature demands a
  zero temperature point.
• Each temperature scale identified one such zero
  temperature point.
• Most popular zero was freezing point of water.
• Knowing the true zero was felt to a scientific
  challenge.

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Ideal Gas Temperature Scale

• This is the most important empirical scale.
• An ideal gas is defined to be one which obeys
  Boyles Law.
• Boyles Law At constant temperature, the volume
  of a gas varies inversely with pressure.
• Mathematically

T is the empirical temperature, a (primitive)
property.
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Gas Thermometers
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Further Experiments on Gas Thermometers
P, kPa
T (0C)
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Further Experiments on Gas Thermometers Unit
mass of Gas at a fixed volume
Gas B
Gas A
P, kPa
Gas C
T (0C)
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Further Experiments on Gas Thermometers Unit
mole of gas
Gas A
Gas B
Gas C
P, kPa
T (0C)
Absolute Zero!
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Further Experiments on Gas Thermometers Unit
mole of gas
P, kPa
T (0C)
Absolute Zero!
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Thermodynamic Temperature

• There is a naturally-defined zero on this scale.
• It is the point at which the pressure of an ideal
  gas is zero, making the temperature also zero
• Thermodynamic temperature is the fundamental
  temperature
• its unit is the Kelvin which is defined as the
  fraction 1/273.16 of the thermodynamic
  temperature of the triple point of water.

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State of A Thermodynamic System

• The collection of all properties for a
  thermodynamic system at a certain condition is
  defined as the state of the system.
• These properties are not independent.
• It was observed that any of them can be expressed
  as a function of some of the others.
• The first three as internal properties of state.
• While the others as called state-functions.
• Internal and external properties of state are
  generically mentioned as variables of state.
• If the variables of state can take arbitrary
  values, they are defined as independent
  variables in the opposite case, they are called
  dependent variables.

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What is the beginning of Happening What is the
culmination of Happening
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Equilibrium

• Frequently we will refer not only to the
  properties of a substance but to the properties
  of a system.
• It is necessarily imply that the value of the
  property has significance for the entire system.
• This implies equilibrium.
• Every system in this universe spontaneously move
  towards equilibrium.

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Thermal Equilibrium

• It is observed that a higher temperature object
  which is in contact with a lower temperature
  object will spontaneously transfer heat to the
  lower temperature object.
• The objects will approach the same temperature,
  and in the absence of loss to other objects, they
  will then maintain a equal temperature.
• They are then said to be in thermal equilibrium.
• Thermal equilibrium refers to equality of
  temperatures.
• Thermal equilibrium is the subject of the
  Temperature measurement.

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Zeroth Law of Thermodynamics

• P M V Subbarao
• Professor
• Mechanical Engineering Department
• I I T Delhi

An Universal Law for Measurement
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Zeroth Law of Thermodynamics

• The "zeroth law" states that two thermodynamic
  systems in thermal equilibrium with the same
  environment are in thermal equilibrium with each
  other.

• If A and C are in thermal equilibrium with B,
  then A is in thermal equilibrium with C. Maxwell
  1872
• Practically this means that all three are at the
  same temperature.
• A basis for comparison of effect of temperatures.
  

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Scottish physicist Joseph Black in his 1786
Lectures on Chemistry, as such There exists
a tendency of heat to diffuse itself from any
hotter body to the cooler around, until it be
distributed among them, in such a manner that
none of them are disposed to take any more heat
from the rest. The heat is thus brought into a
state of equilibrium. This equilibrium is
somewhat curious. We find that when all mutual
action is ended, a thermometer, applied to any
one of the bodies, acquires the same degree of
expansion therefore the temperature of them all
is the same, and the equilibrium is universal.
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Common Thermometers
Liquid in Glass Thermometer
Thermocouple Thermometer
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How Long it takes to Satisfy Zeroth Law?
Conservation of Energy during a time dt
Heat in Change in energy of thermocouple
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Response of Thermo-couple
Define Time constant
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Demonstration of Zeroth Law
If the substance that composes the system is in
thermal equilibrium, the temperature will be the
same throughout the entire system, and we may
speak of the temperature as a property of the
system

• When Two bodies have equality of temperature with
  a third body, they in turn have equality of
  temperature with each other.

BRASS
Copper
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Mechanical Equilibrium

• When Two bodies have equality of pressure with a
  third body, they in turn have equality of
  pressure with each other.

Oxygen Cylinder
LPG Cylinder
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Mechanical Equilibrium of A Finite size System

• If a system is in mechanical equilibrium, there
  is no tendency for the pressure at any point.
• There will be a variation in pressure with
  elevation because of the influence of
  gravitational forces, although under equilibrium
  conditions there will be no tendency for the
  pressure at any location to change.
• In many thermodynamic problems, this variation in
  pressure with elevation is so small that is can
  be neglected.

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Chemical Equilibrium

• A system is in chemical equilibrium when there is
  no tendency for the quantities of species to
  change.
• When Two bodies have equality of concentration
  with a third body, they in turn have equality of
  concentration with each other.

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Chemical Sensors
Can we selectively detect chemicals? Can we
detect classes of chemicals? An electronic
tongue or nose!
Chemical Sensors covers a wide category of
devices used to monitor, measure, test, analyse
concentration.
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Control Methods for Forest Fire
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Thermodynamic Equilibrium

• When a system is in equilibrium regarding all
  possible changes of state, we say that the system
  is in Thermodynamic Equilibrium.
• The properties of a system can be measured, when
  system is at equilibrium.
• Definition of a system using certain observable,
  macroscopic properties is known as description
  of The state.
• Some familiar ones are temperature, pressure, and
  density.
• How many properties are required to completely
  describe the state of a system?

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State Postulate

• The state postulate for a simple, pure substance
  states that the equilibrium state can be
  determined by specifying any two independent
  intensive properties.