Thermal Expansion

Average distance between atoms
Inter-atomic forces

“springs”

- Expansion is directly
- proportional
to temperature change.
Lo
L
DL
Δℓ = αℓ0ΔT
α: the Coefficient of
linear expansion
L0: Initial length of the
object
ΔL: Length change of
the object
ΔT: Temperature
change of the object

A solid expands when heated,
contracts when its temperature
decreases.
Ball and Ring
Before heating the ball After heating the ball

Areas expand twice as much as lengths
do.
ΔA = 2αA0ΔT
A
Ao
α : the Coefficient of
Area expansion
A0: Initial area of the
object
ΔA: Area change of
the object
ΔT: Temperature

Every linear
dimension increases
by the same
percentage with a
change in
temperature,
including holes.
This assumes that the
expanding material is
uniform.

Volumes expand three times as much as
lengths do. ΔV = 3αV0ΔT
Vo
V
α : the Coefficient of
volume expansion
V0: Initial volume of
the object
ΔV: Volume change
of the object
ΔT: Temperature

Coefficient of Volume Expansion
• For small volume changes the
relationship between volume and
temperature is linear.
• The coefficient of volume
expansion is b.
Material Coefficient b
Quartz 1 x 10-6 C-1
Pyrex glass 9 x 10-6 C-1
Glass 27 x 10-6 C-1
Steel 35 x 10-6 C-1
Aluminum 75 x 10-6 C-1
Mercury180 x 10-6 C-1
Water 210 x 10-6 C-1
Gasoline950 x 10-6 C-1
Ethyl alcohol 1100 x 10-6 C-1
Air (1 atm) 3400 x 10-6 C-1
TVV DD 0b

PV = nRT PV = NkT
P
absolute
pressure
T
absolute
temperature
V volume
n number of moles
R
gas constant
= 8.315 J/mol K
N = number of particles
k = Boltzmann's constant = 1.382 × 10
−23
J/K
P
absolute
pressure
T
absolute
temperature
V volume

A segment of steel railroad track
has a length 30.000m, when the
temperature is 0.0 C
What is the length when
temperature is 40.0 C?
steel railroad (11 x 10-6 C-1 )

Solution:
DL = L0  DT)
DL = ( 11 x 10-6 C-1 )
(30.000m) ( 40oC )
= 0.013 m
L = 30.013 m

• The steel bed (12 x 10-6 C-1 ) of a
suspension bridge is 200 m long at 20 C.
• If the temperature goes from -30 C to
+20 C, what contraction and expansion is
possible?

Using Linear Expansion.
Solve for DL = L0 DT.
Solution:
First in winter,
DL = (12 x 10-6 C-1)(200 m)(-50 C)
DL = -0.12 m
Then in summer,
DL = (12 x 10-6 C-1)(200 m)(20 C)
DL = 0.048 m

A surveyor uses a steel measuring
tape that is exactly 50.000 m at a
temperature of 20 oC. What is the
length on a hot summer day when the
temperature is 35 oC?
steel = 1.210-5 K-1

Given:
L0 = 50 .000 m
DT = 15 oC
 = 1.210-5 K-1
Solution:
DL = L0  DT
DL = 50.000m(1.210-5 K-1 )(15 oC )
= 50.009 m

• A 72 L steel gas tank is open and filled to the
top with gasoline, b = 950 x 10-6 C-1, at 18 C.
The car sits in the sun and reaches a
temperature of 32 C.
• How much gasoline overflows from the tank?

The gasoline expands with temperature.
Solve for DV = bV0 DT.
Solution:
DV = (950 x 10-6 C-1)(72 L)(14 C)
DV = 0.96 L

Thermal Expansion
• Bridges are built with ‘joints’ so they don’t
crack when the temperature changes.

BECAUSE STEEL HAS A
RELATIVELY HIGH
COEFICIENT OF
THERMALEXPANSION ,
STANDARD RAILROAD
TRACKS ARE
CONSTRUCTED SO THAT
THEY CAN SAFELY
EXPAND ON A HOT DAY
WITHOUT DERAILING
THE TRAINS TRAVELING
OVER THEM .

A MAN ICE FISHING
IN MONTANA .
BECAUSE OF THE
UNIQUE THERMAL
EXPANSION
PROPERTIES OF
WATER , ICE FORMS
AT THE TOP OF A
LAKE RATHER THAN
THE BOTTOM , THUS
ALLOWING MARINE
LIFE TO CONTINUE
LIVING BELOW ITS
SURFACE DURING
THE WINTER .

33
Two strips of different metals welded
together at one temperature become
more or less curved at other
temperatures because the metals have
different values for their coefficient of
linear expansion .
They are often used as thermometers
and thermostats
lower metal expands more
than upper metal when
heated
Q

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Vol-2/Thermal-Expansion-How-it-works.html#ixzz3hKvveco9
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Thermal Expansion

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