Zeroth Law of Thermodynamics

P M V SubbaraoProfessor

Mechanical Engineering Department

I I T Delhi

An Universal Law for Measurement …

Textbook of Materials & Metallurgical Thermodynamics by Ahindra Ghos

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

• Every system in this universe spontaneously move towards equilibrium.

• Thermal equilibrium refers to equality of temperatures.

• Thermal equilibrium is the subject of the Temperature 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

How Long it takes to achive Zeroth Law?

Conservation of Energy during a time dt

Heat in = Change in energy of thermocouple

System theof eTemperatur ousInstantanetTs

tTs tTth

r thermmeteof eTemperatur ousInstantanetTth

ththththsb dTCVdtTTUA

thsbth

thth TTUAdt

dTCV

sthth

b

thth TTdt

dT

UA

CV

b

ththth

UA

CV Define Time constant

sthth TT

dt

dT

s

Tsss s

thth

s

Tss s

th 1 1

ss

Ts s

th

Sudden Immersion of Thermometer in a Known Constant Temperature System

sbthbth

thth TUATUAdt

dTCV

1

s

T

s

Ts ss

th

1

s

T

s

Ts ss

th

1

11

ss

Ts sth

1

111

ss

TtT sth

t

TtT sth exp1

t

TtT sth exp1

b

ththth

UA

CV

ttTth exp1

Ts

Response of A Thermo-couple in A Constant Temperature System

Ts

tTtc

t

Response of A Thermo-couple in A Ramp Temperature System

tTtc

t

Ts(t)=Ct

Temperature Scales Significance of Temperature Kelvin

5,780.07 K Black body temperature of visible surface of Sun

3,683.02 K Freezing point of tungsten

1,941.07 K Freezing point of titanium

1,357.77 K Standard freezing point of copper

1,337.33 K Standard freezing point of gold

1,234.93 K Standard freezing point of silver

933.47 K Standard freezing point of aluminum

692.68 K Standard freezing point of zinc

505.08 K Standard freezing point of tin

429.75 K Standard freezing point of indium

373.15 K Standard boiling point of water

330.93 K World record high air temperature

Imapact of Zeroth Law: Creation of Temperatures

Outcome of Zeroth Law : Gas Thermometers

Further Experiments on Gas Thermometers

T (0C)

p, kPa

CTpp 0

Further Experiments on Gas Thermometers

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~

Saturated Liquid Nitrogen at 1 atm

Saturated Liquid Nitrogen

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

A Journey tow Zeroards Absolute