Lecture 10
HEAT
Phases of matter
Temperature
Temperature Scales
Thermal expansion
Phases of matter
Solid
rigid
retains shape
Molecules
linked by spring-like forces
average positions fixed
Liquid
flows
 does not retain shape.
Molecules
 freer to move
remain close to each other
Gas
flows
does not retain shape
Molecules
move anywhere
 little interaction
Temperature and Heat
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
Temperature is a characteristic of an object
related to the average kinetic energy of
atoms and molecules of the object.
Heat
Energy exchange between two objects at
different temperatures
Temperature
Temperature is a measure of the average
kinetic energy of atoms and molecules.
Robert Brown, botanist noticed in 1828
that tiny particles (pollen grains) exhibited
an incessant, irregular motion in a liquid.
Brownian motion
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”
A suspended small particle is constantly
and randomly bombarded from all sides
by molecules of the liquid.
indirect confirmation of existence of
molecules and atoms
Temperature and Heat
Brownian motion
polystyrene particles, 1.9 mm in diameter, in
water
T = 25 C
in any short period of time
•random number of impacts
•random strength
•random directions
Brownian motion is a clear demonstration of the
existence of molecules in continuous motion
Temperature scales
There are 3 temperature scales:
Anders Celsius (1701-1744)
- Celsius (C)
Gabriel Fahrenheit (1686 -1736) - Fahrenheit (F)
Lord Kelvin (1824-1907)
- Kelvin (K)
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):
Freezing point of water: 0C or 32F
Boiling point of water: 100C or 212F
Range- freezing to boiling point of water
Celsius, 100 degrees. Fahrenheit, 180 degrees
Temperature scales
Water
Boiling
100
212
Freezing
0
32
Absolute
zero
-273.15
-459.69
373.15
273.15
0
CelsiusoC Fahrenheit oF Kelvin, K
(absolute)
Absolute zero:
Temperature at which all thermal motion ceases
Room temperature 20o Celsius
68o Fahrenheit
293 Kelvin
SI unit of temperature is the Kelvin
Temperature scales
Gas pressure depends on temperature
Example
Tyres have higher pressure when hot
compared with cold.
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.
Most gases at atmospheric pressure and
room temperature behave approximately
as ideal gases
Kelvin Temperature Scale
Ideal gas
Constant volume
Constant pressure
P
V
-273.15
-200
-273.15
T oC
200
Linear relationship
exists between pressure
and temperature at
constant volume
-200
T oC
200
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
Kelvin Temperature Scale
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 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
Kelvin (K) scale
●same basic unit size as Celsius
T K   T C   273.15
Example:
Freezing point of water : 273.15 K
Boiling point of water:
373.15 K
Converting Temperatures
Celsius to Fahrenheit :
T F   9 T C   32
5
Fahrenheit to Celsius :
T C   5 T F   32
9
Celsius and Fahrenheit scales allow for negative
temperature
Thermometers
•Alcohol in glass
•Mercury in glass
Depends on thermal expansion
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.
T C   5 T F   32
9
T C   5 98.6F   32  37oC
9
T C   5 107F   32  41.7oC
9
Difference DT(0C)= [41.7-37]0C = 4.70C
T K   T C   273.15
T K   37C   273.15  310.15K
T K   41.7C   273.15  314.85K
Difference DT(K) = [314.85-310.15]K = 4.7K
Temperature and Heat
Applications
Oral environment
temperature is not constant;
Hot and cold food and drink
Dental pulp is sensitive, may be damaged if
its temperature increases >5oC)
Dental drilling
Rise in temperature of pulp during drilling
should be less than 5 oC
Dental materials: Important characteristics
transfer of heat
Dimensional changes: expansion and contraction
Thermal expansion
Most materials
•expand when temperature is increased
•contract when temperature is decreased
this is called thermal expansion and contraction
Low Temperature
High Temperature
Origin: When the average kinetic energy (or
‘speed’) of atoms is increased, they
experience stronger collisions, increasing the
separation between atoms.
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.
Thermal expansion
Temperature T
L
Temperature (T  DT )
DL
L  DL
Bar of initial length L changes by an amount DL
when its temperature changes by an
amount DT.
Coefficient of linear expansion a for the material
is defined as:
Fractional change in length
a=
Change in temperature
DL/L

DT
Thermal expansion
linear expansion:
DL  (L)(a )(DT )
units
m
m
oC-1
or K-1 C or K
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.
*Temperature interval is the same for
Celsius and Kelvin scales
Thermal expansion
Important in dental restorations
Decayed dentine removed and replaced
by filling.
Coefficient of thermal expansion of the
restorative material should be similar
to that of the tooth
Thermal expansion/contraction due to hot and
cold foods should not cause separation
at the tooth-filling interface
Large mismatch in expansion coefficients:
•Fluids leakage between filling and surrounding
tooth
Thermal expansion
Dimensional changes minimised by
transient nature of thermal stimuli
relatively low “thermal diffusivity” of non-metallic
restorative materials
Example
10oC temperature change for 1 sec
Little change in bulk material dimensions
Coefficient of Thermal linear expansion
Enamel Dentine
Amalgam Composite
filling
material
Gold
11.4* x 8.3 X
10-6 K-1 10-6 K-1
25 x
10-6 K-1
14.5x
10-6 K-1
≈ 30 x
10-6 K-1
Composite material: repeated thermal cycling:
bonded joint between the filling and the tooth
may loosen.
Thermal expansion
Coefficient of Thermal linear expansion
Enamel Dentine
Amalgam Composite
filling
material
11.4 x
8.3 X
10-6 K-1 10-6 K-1
25 x
10-6 K-1
≈30 x
10-6 K-1
Gold
14.5x
10-6 K-1
Example
Amalgam 8 mm wide, oral temperature
decreases by 5 oC. Calculate relative thermal
contraction.
DL  (L)(a )(DT )
Amalgam contracts by
DL  (8mm)(25 106 C 1 )(5 oC )  110 3 mm
Tooth enamel contracts by
DL  (8mm)(11.4 106 C 1 )(5 oC )  0.45 103 mm
Relative thermal contraction = 0.55 mm
Thermal expansion
Application
Thermostat
Thermally activated
Electrical switch
Bimetallic strip
brass
steel
20oC
Switch closed
Brass has larger
coefficient of thermal
expansion
23oC
Switch open
Mercury or Alcohol thermometer
.
−
Why is there a reservoir at the
bottom of a thermometer?
−
−
−
−
amercury = 60 x 10-6 °C-1
−
−
Column
Assume
length of the column is 10cm,
range of temperature is 35 to 43°C,
−
−
−
−
−
−
−
−
thermal expansion of the column is:
−
−
Reservoir
DL  ( L)(a )(DT )  (0.1m)(60 x 10-6 )(8.0)
DL  4.8 x 10 m = 0.048mm
-5
This increase in length due to thermal
expansion would never be visible using a
simple column.
Adding a reservoir increases the volume
of mercury and thus the expansion.
Area Thermal expansion
linear thermal
expansion:
T
T+DT
DL  ( L)(a )(DT )
L  L  DL
area thermal expansion:
DA = ?
A  A  DA
Consider square, side length L, area A = L2
New area: A+ DA = (L+ DL)2 = L2 + 2L DL + DL2
A+ DA ≈ L2 + 2L DL
Thus DA = 2L DL = 2L(LaDT)
DA = L2(2a)DT = A(2a)DT
Thus, the coefficient of area expansion is
approximately 2a
Volume expansion
DV = V(g)DT
g = coefficient of volume
expansion
Example
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)
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:
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?
Coefficient of linear expansion of steel
a = 1.2 x10-5 oC-1
DL  ( L)(a )(DT )
DL = (50 m)(15oC)(1.2x10-5 oC-1)
DL = 900x10-5m =0.009m
Length of tape at 35oC = 50.009m
20oC
35oC
50.009m (35.694m) = 35.700m
50.0000
Error =6mm
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.
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  ( L)(a )(DT )
DT =600C
DL = 25m*12x10-6(0C-1)* 600C = 18 x10-3m