Quantification of Macroscopic PropertyTheory Vs Practice

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

An Effort to Develop Some Understanding about System…

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.

p-v-T Diagram of solid Phase

Top View : V – T Diagram

Front View : p – V Diagram

Volume

Temperature

Pressure

Mathematical description of A Substance

Identification of Phase of A Substance:

β ≈ 10−3/K for liquids β ≈ 10−5/K for solids

p-v-T Diagram of H2O

Global Change in any Selected Property – Type I

Given a path p=f(T), to evaluate

dTTpNdpTpMdhh ),(),( From A to B.

)('

)),(()),((Tf

dpTTfNdpTTfMh

Global Change in any Selected Property – Type II

dTTpNdpTpMdhh ),(),(

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.

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.

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”

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.

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

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.

Newton’s 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.

A plausible 'wind tunnel' for Newton's coolingexperiments.

Newton’s 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.

Newton’s 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

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.

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.

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

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.

Temperature Scales Significance of Temperature

Fahrenheit Celsius Kelvin

9,944.45°F 5,506.92°C 5,780.07 K Black body temperature of visible surface

of Sun

6,169.76°F 3,409.87°C 3,683.02 K Freezing point of tungsten

3,034.26°F 1,667.92°C 1,941.07 K Freezing point of titanium

1,984.32°F 1,084.62°C 1,357.77 K Standard freezing point of copper

1,947.53°F 1,064.18°C 1,337.33 K Standard freezing point of gold

1,763.20°F 961.78°C 1,234.93 K Standard freezing point of silver

1,220.58°F 660.32°C 933.47 K Standard freezing point of aluminum

787.15°F 419.53°C 692.68 K Standard freezing point of zinc

449.47°F 231.93°C 505.08 K Standard freezing point of tin

313.88°F 156.60°C 429.75 K Standard freezing point of indium

212°F.00 100°C.00 373.15 K Standard boiling point of water

136°F.00 57.78°C 330.93 K World record high air temperature

98.60°F 37°C.00 310.15 K Human body temperature reference 85.58°F 29.76°C 302.91 K Standard melting point of gallium 68°F.00 20°C.00 293.15 K Room temperature reference 39.15°F 3.97°C 277.12 K Temperature of maximum water density 32.02°F 0.01°C 273.16 K Triple point of water 32°F.00 0°C.00 273.15 K Standard freezing point of water 0°F.00 -17.78°C 255.37 K Fahrenheit's zero -37.90°F -38.83°C 234.32 K Triple point of mercury -128.56°F -89.20°C 183.95 K World record low air temperature -308.82°F -189.34°C 83.81 K Triple point of argon -361.82°F -218.79°C 54.36 K Triple point of molecular oxygen -415.47°F -248.59°C 24.56 K Triple point of neon -434.82°F -259.35°C 13.80 K Triple point of molecular hydrogen -459.67°F -273.15°C 0 K.00 Thermodynamic absolute zero

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.

The relation between Pressure & Temperature

What is Temperature Really?

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

n

ii

n

iii

m

vmT

1

1

2

21

• When atoms collide they tend on the average, to equalize kinetic energy spreads equally over all atoms.

• This is called thermal equilibrium.

Temperature Measuring Devices

Liquid in glassBimetallicGas thermometers ThermocoupleResistance Temperature DetectorsRadiation and optical pyrometers

Liquid in Glass Thermometer

initialfinalinitialfinal TTVV 1

44

22capillary

initialfinalcapillary

initialfinal

d

Vll

d

VVl

4

2capillary

initialfinalinitialinitialfinal d

TTVll

Material Coefficient of Volumetric Thermal Expansion in 10-6 /K

Mercury 180

Ethyl Alcohol 1120

petrol 950

Water 0 to 695 (4 to 90 0C)

Glass 9.9

Bimetallic Expansion Thermometer

A Measure of TemperatureMaterial in 10-6 /K

Chromium

4.9

Copper 16.5

lead 28.9

Zinc 30.2

Thermocouple

njnjjjj TbTbTbbTFE .....2

2100

Standard Thermocouples• The ASTM identifies eight standard types of thermocouples.

Thermocouple temperature vs.Voltage graph

Resistance Temperature Device

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a

b

c

1 52 3 6 74

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.

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.

05

2

0 1

12,

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e

hcdTI

kT

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4

42

15

2TT

khc

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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.

Ideal Gas Temperature Scale

• This is the most important empirical scale.

• An ideal gas is defined to be one which obeys Boyle’s Law.

• Boyle’s Law: At constant temperature, the volume of a gas varies inversely with pressure.

• Mathematically:

Constant1

pvv

p

T is the empirical temperature, a (primitive) property….

TfC

Gas Thermometers

Further Experiments on Gas Thermometers

T (0C)

P, kPa

CTpp 0

Further Experiments on Gas Thermometers : Unit mass of Gas at a fixed volume

T (0C)

P, kPa

Gas A

Gas B

Gas C

Absolute Zero!

Further Experiments on Gas Thermometers : Unit mole of gas

T (0C)

P, kPa

Gas A

Gas BGas C

Absolute Zero!

Further Experiments on Gas Thermometers : Unit mole of gas

T (0C)

P, kPa

Absolute Zero!

TRp~

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.

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.

What is the beginning of Happening ……What is the culmination of Happening ……

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.

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.

Zeroth Law of Thermodynamics

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

An Universal Law for Measurement …

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.

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.”

Common Thermometers

Liquid in Glass Thermometer Thermocouple Thermometer

How Long it takes to Satisfy Zeroth Law?

Conservation of Energy during a time dt

Heat in = Change in energy of thermocouple

System theof eTemperatur ousInstantanetTs

tTs tTtc

ple thermocouof eTemperatur ousInstantanetTtc

stctctctc

tctc TUATUAdt

dTCV

Response of Thermo-couple

tc

tctc

UA

CVT

Define Time constant

Demonstration of Zeroth Law

When Two bodies have equality of

temperature with a third body, they in

turn have equality of temperature with each

other.BRASSCopper

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

Mechanical Equilibrium

When Two bodies have equality of pressure with a third body, they in turn have

equality of pressure with each other.

LPG CylinderOxygen Cylinder

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.

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.

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.

Control Methods for Forest Fire

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?

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.