Methods & Means for Property Measurement &Need For A Law

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

Be Cautious, while Numerically Describing a Macroscopic Property…

…

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

C

33.2096 C

69.3774

Multiple Options :Temperature Measuring Devices

Liquid in glassBimetallicThermocoupleResistance Temperature DetectorsRadiation and optical pyrometersGas thermometers

Liquid in Glass Thermometer

initialfinalinitialfinal TTVV 1

4

2capillary

initialfinal

d

VVl

4

2capillary

initialfinal d

Vll

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

Free End

At Reference Temperature

At Higher Temperature

A Measure of Temperature

Material in 10-6 /K

Chromium 4.9

Copper 16.5

lead 28.9

Zinc 30.2

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 be 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~

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

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, by making the temperature also zero

• Thermodynamic temperature is the fundamental empirical 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.

How to use these quantified macroscopic properties to identify a

Thermodynamic System ?

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 ……

Scottish physicist Joseph Black

• On returning to Glasgow as professor in 1756, Black met up with James Watt ("mathematical instrument maker to the University").

• This meeting stimulated the next phase of his work involving the concept of latent heat, and the first steps in calorimetry.

• Here again, it was the quantitative aspects of his work which led to his discoveries, particularly in the careful measurement of heat.

• "He waited with impatience for the winter" in Glasgow so that he could do experiments on the freezing and melting of water and water/alcohol mixtures that led to the concept of latent heat of fusion.

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.”

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

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.

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