Phases of matter

Temperature

Temperature Scales

Thermal expansion

HEAT

Lecture 10

Phases of matter

flows

does not retain shape

Molecules

move anywhere

little interaction

flows

does not retain shape.

Molecules

freer to move

remain close to each other

Solid

Liquid

Gas

rigid

retains shape

Molecules

linked by spring-like forces

average positions fixed

Molecules are in constant disordered motion

Velocities distributed over a large range

Average kinetic energy directly related

to temperature

Greater their average kinetic energy

•Higher the temperature

Heat

Energy exchange between two objects at

different temperatures

Temperature is a characteristic of an object

related to the average kinetic energy of

atoms and molecules of the object.

Temperature and Heat

Temperature is a measure of the average

kinetic energy of atoms and molecules.

Brownian motion

A suspended small particle is constantly

and randomly bombarded from all sides

by molecules of the liquid.

Temperature

Robert Brown, botanist noticed in 1828

that tiny particles (pollen grains) exhibited

an incessant, irregular motion in a liquid.

Remained largely unexplained until

Einstein paper in 1905

“On the motion of small particles suspended

in a stationary liquid demanded by the

molecular-kinetic theory of heat”

indirect confirmation of existence of

molecules and atoms

Temperature and Heat

polystyrene particles, 1.9 mm in diameter, in

water

T = 25 C

Brownian motion is a clear demonstration of the

existence of molecules in continuous motion

in any short period of time

•random number of impacts

•random strength

•random directions

Brownian motion

There are 3 temperature scales:

Anders Celsius (1701-1744) - Celsius (C)

Gabriel Fahrenheit (1686 -1736) - Fahrenheit (F)

Lord Kelvin (1824-1907) - Kelvin (K)

Temperature scales

Differ by (a) the basic unit size or degree ()

(b) lowest & highest temperature

Celsius and Fahrenheit are defined by the

freezing point and the boiling point of water

(at standard atmospheric pressure):

Range- freezing to boiling point of water

Celsius, 100 degrees. Fahrenheit, 180 degrees

Freezing point of water: 0C or 32F

Boiling point of water: 100C or 212F

CelsiusoC Fahrenheit oF Kelvin, K

(absolute)

212

32

373.15

273.15

100

0 Freezing

Boiling

Water

0 -459.69 -273.15 Absolute

zero

SI unit of temperature is the Kelvin

Temperature scales

Room temperature 20o Celsius

68o Fahrenheit

293 Kelvin

Absolute zero:

Temperature at which all thermal motion ceases

Gas pressure depends on temperature

Example

Tyres have higher pressure when hot

compared with cold.

Temperature scales

Most gases at atmospheric pressure and

room temperature behave approximately

as ideal gases

Ideal gas:

Is a collection of atoms or molecules

• move randomly

•considered to be point-like

•exert no long-range forces on each other.

•occupy negligible volume.

T oC 200 -200

-273.15

P

T oC 200 -200

-273.15

V

Kelvin Temperature Scale

Ideal gas

Linear relationship

exists between pressure

and temperature at

constant volume

Linear relationship

exists between volume

and temperature at

constant pressure

All plotted lines extrapolate to a temperature

intercept of -273.15 oC regardless of initial

low pressure (or volume) or type of gas

Unique temperature called absolute zero

Fundamental importance

Constant volume Constant pressure

Kelvin (K) scale

●same basic unit size as Celsius

15.273 CTKTExample:

Freezing point of water : 273.15 K

Boiling point of water: 373.15 K

Unique temperature of -273.15oC is called

absolute zero,

below which further cooling will not occur

Fundamental importance and the basis of the

Kelvin temperature scale

Kelvin Temperature Scale

Kelvin Scale defined by 2 points.

absolute zero -273.15oC

Triple point of water- temperature at which

3 phases, solid, liquid, and gas are in equilibrium

0.01 oC

Celsius and Fahrenheit scales allow for negative

temperature

Fahrenheit to Celsius :

Celsius to Fahrenheit :

Converting Temperatures

Thermometers

•Alcohol in glass

•Mercury in glass

Depends on thermal expansion

325

9 CTFT

329

5 FTCT

Example.

Body temperature can increase from 98.60F to

1070F during extreme physical exercise or during

viral infections. Convert these temperatures to

Celsius and Kelvin and calculate the

difference in each case.

CFCT o7.41321079

5

CFCT o37326.989

5

KCKT 15.31015.27337

KCKT 85.31415.2737.41

329

5 FTCT

Difference DT(0C)= [41.7-37]0C = 4.70C

Difference DT(K) = [314.85-310.15]K = 4.7K

15.273 CTKT

Dental pulp is sensitive, may be damaged if

its temperature increases >5oC)

Temperature and Heat

Dental drilling

Rise in temperature of pulp during drilling

should be less than 5 oC

Applications

Oral environment

temperature is not constant;

Hot and cold food and drink

Dental materials: Important characteristics

transfer of heat

Dimensional changes: expansion and contraction

Origin: When the average kinetic energy (or

‘speed’) of atoms is increased, they

experience stronger collisions, increasing the

separation between atoms.

Most materials

•expand when temperature is increased

•contract when temperature is decreased

Low Temperature High Temperature

Thermal expansion

this is called thermal expansion and contraction

Thermal expansion

Thermal expansion depends on:

•Material

•Size,

•Temperature change.

Assume no change in phase

Linear Thermal Expansion

Important, for example, for metals in buildings,

bridges and dental filling materials etc.

a = Fractional change in length

Change in temperature

DL/L

DT

Coefficient of linear expansion a for the material

is defined as:

Bar of initial length L changes by an amount DL

when its temperature changes by an

amount DT.

Thermal expansion

L

T

( )T T D

L L D

LD

Temperature

Temperature

m m C or K

Thermal expansion

( )( )( )L L TaD D

DL = change in length

L = original length

DT = change in temperature (C or K)

a coefficient of linear expansion

units (°C-1 or K- 1)*

a depends on the type of material.

linear expansion:

oC-1 or K-1

*Temperature interval is the same for

Celsius and Kelvin scales

units

Thermal expansion

Decayed dentine removed and replaced

by filling.

Thermal expansion/contraction due to hot and

cold foods should not cause separation

at the tooth-filling interface

Coefficient of thermal expansion of the

restorative material should be similar

to that of the tooth

Important in dental restorations

Large mismatch in expansion coefficients:

•Fluids leakage between filling and surrounding

tooth

Thermal expansion

Coefficient of Thermal linear expansion

Enamel Dentine

Amalgam Composite

filling

material

Gold

11.4* x

10-6 K-1

8.3 X

10-6 K-1

25 x

10-6 K-1

≈ 30 x

10-6 K-1

14.5x

10-6 K-1

Composite material: repeated thermal cycling:

bonded joint between the filling and the tooth

may loosen.

Dimensional changes minimised by

transient nature of thermal stimuli

relatively low “thermal diffusivity” of non-metallic

restorative materials

10oC temperature change for 1 sec

Little change in bulk material dimensions

Example

Thermal expansion

Example

Coefficient of Thermal linear expansion

Enamel Dentine

Amalgam Composite

filling

material

Gold

11.4 x

10-6 K-1

8.3 X

10-6 K-1

25 x

10-6 K-1

≈30 x

10-6 K-1

14.5x

10-6 K-1

Amalgam 8 mm wide, oral temperature

decreases by 5 oC. Calculate relative thermal

contraction. ( )( )( )L L TaD D

6 1 3(8 )(25 10 )(5 ) 1 10oL mm C C mm D

Tooth enamel contracts by 6 1 3(8 )(11.4 10 )(5 ) 0.45 10oL mm C C mm D

Relative thermal contraction = 0.55 mm

Amalgam contracts by

Thermal expansion

Application Thermostat

Thermally activated

Electrical switch

Bimetallic strip

20oC

Switch closed

23oC

Switch open

Brass has larger

coefficient of thermal

expansion

brass

steel

This increase in length due to thermal

expansion would never be visible using a

simple column.

Why is there a reservoir at the

bottom of a thermometer?

Reservoir

Column

amercury = 60 x 10-6 °C-1

Assume

length of the column is 10cm,

range of temperature is 35 to 43°C,

thermal expansion of the column is:

Mercury or Alcohol thermometer

-6( )( )( ) (0.1m)(60 x 10 )(8.0) L L TaD D

-5 4.8 x 10 m = 0.048mmLD

Adding a reservoir increases the volume

of mercury and thus the expansion.

. −

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

−

linear thermal

expansion:

Consider square, side length L, area A = L2

New area: A+ DA = (L+ DL)2 = L2 + 2L DL + DL2

A+ DA ≈ L2 + 2L DL

area thermal expansion:

DA = ?

( )( )( )L L TaD D L L L D

Area Thermal expansion

A A A D

T T+DT

Thus DA = 2L DL = 2L(LaDT)

DA = L2(2a)DT = A(2a)DT

Thus, the coefficient of area expansion is

approximately 2a

Volume expansion

Example

DV = V(g)DT

A 50 ml glass container is filled to the brim

with methanol at 0.0oC. If the temperature is

raised to 40oC will any methanol spill out? If so,

how much?

g glass ≈ 9 x10-6 (oC-1)

g methanol ≈ 1200 x10-6 (oC-1)

g = coefficient of volume

expansion

Volume spilled = DV(methanol) – DV(glass)

DV(glass) = 50.0ml(9 x10-6 (oC-1)(40oC)

= 0.018ml

DV(methanol) = 50.0ml(1200 x10-6 (oC-1)(40oC)

= 2.4ml

Therefore

2.4ml – 0.018ml = 2.38 ml will spill out

Exercise:

DL = (50 m)(15oC)(1.2x10-5 oC-1)

A steel measuring tape used by a civil engineer

is 50metres long and calibrated at 20oC.

The tape measures a distance of 35.694m

at 35oC. What is the actual distance measured?

( )( )( )L L TaD D

Coefficient of linear expansion of steel

a = 1.2 x10-5 oC-1

DL = 900x10-5m =0.009m

Length of tape at 35oC = 50.009m

20oC

35oC

Error =6mm

(35.694m) = 35.700m 50.009m 50.0000

Example.

Concrete slabs of length 25 m are laid end to end

to form a road surface. What is the width of the

gap that must be left between adjacent slabs at a

temperature of -150C to ensure they do not buckle

at a temperature of +450C.Coefficient of thermal

expansion for concrete a = 12x10-6 0C

Slabs should barely touch at the higher

temperature.

( )( )( )L L TaD DDT =600C

Each slab must expand at either end by an

amount equal to half the gap. The total expansion

of each slab should be equal to the gap.

DL = 25m*12x10-6(0C-1)* 600C = 18 x10-3m