Transcript No Slide Title

Thermal Expansion
•the expansion or contraction of
objects due to heat in or out
•Generally speaking:
•Heat in > expansion!
•Heat out > contraction!
Thermal Expansion
Thermal Energy the total PE and KE that is
associated with the molecules of a substance
• depends upon mass, type of substance,
and the temperature it is at
Heat the transfer of thermal energy-- thermal
energy goes out of one body and into some other
• thermal energy is always exchanged from
higher temperature to lower temperature
• temperature reflects the the direction in
which heat energy will flow
20˚C
100˚C
• The heat will flow from the higher temperature to
the lower one regardless of mass or substance!
Temperature What the hell does it measure?
• NOT a measure of heat or thermal energy!
• is a reflection of the average KE of the
molecules of a substance (KE = .5mv2)
• therefore, if the temperature is changing, the
speed of the molecules is changing!
Temperature Scales
• There are 3 common temperature scales:
Farenheit (˚F), Celsius (˚C), and Kelvin (˚K)
• The Celsius scale is based upon the triple point of
water-- the temp./pressure combination where
water will coexist in all 3 phases!
•The Kelvin scale is based upon the
theoretically lowest possible temperature-absolute zero.
Absolute zero (0˚K)-- the temperature at which
molecular motion (and KE) will be the least.
• A ˚K and a ˚C have the same magnitude.
˚K = ˚C + 273
Measuring Heat
• We do not directly measure the thermal energy
of a substance.
• We, instead, measure the effects of heat- thermal
energy transferring from one substance to another.
• Heat is sometimes measured in calories
‡a calorie was originally defined as the amount
of heat needed to raise 1 g of H2O up 1 ˚C
• Since heat is a form of energy, it is measured in
Physics in Joules
4.19 J = 1 cal
One effect of heat is Thermal Expansion
• When heat is absorbed by a substance, the
molecules of the substance move faster and also
spread out.
• The opposite occurs when the substance loses
heat.
How much a substance will expand or contract
depends upon 3 things:
type of material
temperature change
original size
A notable exception to the rule of thermal
expansion is …..
WATER
Because God is not a DUMBASS!
if HE were like you:
because he is NOT:
water:
100˚C
contracts
4˚C
expands !
0˚C
Thermal expansion of solids depends upon:
• original length-- l
• temperature change-- ∆T = Tf - Ti
• the rate at which the material will expand per ˚C
per original length:
the coefficient of linear expansion ()
 = ∆l
l•∆T
units:
per ˚C
If we are concerned about the area that a solid is
expanding:
area expansion = 2
If we are concerned about the volume that a solid
is expanding:
volume expansion = 3
MATERIAL
Aluminum
Brass
Iron (steel)
Glass (Pyrex)
Glass (ordinary)
Quartz
α (C˚) -1
25 x 10-6
19 x 10 -6
12 x 10 -6
3 x 10-6
9 x 10 -6
0.4 x 10-6
An aluminum rod is initially 5.000 m long at 20.0
˚C. How long will the rod be when heated to a
temperature of 100.0 ˚C?
= 25 X 10-6 /˚C
l = 5.000 m
Ti = 20.0˚C
l = ?
Tf = 100.0˚C
∆l = • l∆T
=(25 X 10-6/˚C)(5.000 m)(80.0˚C)
= .0100 m
l = l + ∆l = 5.000 m + .0100 m
= 5.010 m
Thermal expansion of liquids depends upon:
• original volume-- V
• temperature change-- ∆T = Tf - Ti
• the rate at which the material will expand per ˚C
per original volume:
the coefficient of volume expansion ()
 = ∆V
V•∆T
units:
per ˚C
Sample Coefficients of Volume Expansion
MATERIAL
Gasoline
Acetone
Mercury
Ethyl Alcohol
Glycerin
Water
β (C˚) -1
950 x 10-6
1500 x 10-6
180 x 10-6
1100 x 10-6
500 x 10-6
210 x 10-6
2.000 L of a liquid will expand to a volume of
2.119 L when heated from 25.0 ˚C to 65.0˚C.
What must this liquid be?
V = 2.000 L
V = 2.119 L
Ti = 25.0 ˚C
Tf = 65.0 ˚C
=?
∆V = .119 L
∆T = 40.0 ˚C
 = ∆V
V∆T
= .119 L
(2.000 L)(40.0˚C)
1.49 X 10-3 /˚C
=1490 X 10-6/˚C
acetone
A steel rivet that is 1.871 cm in diameter at 20.0˚C
needs to be cooled to what temperature so that it
will fit in the rivet hole which is 1.869 cm?
A steel rod and a brass rod are each exactly 25.000
cm long at 20.0˚C. Both are then heated to 100.0˚C.
Which rod is longer and how much longer is it?
How much gas will spill out of a 12.00 L if it is
filled to capacity at 0.0˚C and heated to 75.0˚C?
Assume the tank is made out of some magic stuff
that won’t expand at all. Happens everyday.
A glass (α = 9 X 10-6/˚C) beaker that is 1000.0
cm3 is filled to the brim with ethyl alcohol (β =
1100 X 10-6/˚C) at 20.0˚C. It is then heated to
99.0˚C. How much alcohol will spill out of the
beaker?
On the coldest day of the year in Chicago history
(-33˚C) the height of the Sears tower was
measured to be 1450 ft. What would the height
have been if it were measured on the hottest
(40.5˚C) day of the year? Assume the tower is
made of steel (β = 12 X 10-6/˚C).
Thermal Expansion of Gases
• Because gas molecules act as independent
particles, all gases expand and contract at the
same rate
 1/273 of the volume of the gas at STP
per every ˚C
• This relationship was demonstrated by Jacques
Charles and is known as Charles’ Law:
 the volume of a gas is directly
proportional to the Kelvin Temp.
Charles Law:
V = V
Tk
Tk
This is only true assuming the pressure on the gas
remains constant, which it often does not!
The effect of pressure on a gas while the
temperature remains constant was first
demonstrated by Robert Boyle:
Boyle’s Law: the volume of a gas varies
inversely with the pressure on it!
Boyle’s Law:
PV = P V
When the pressure and the temperature changing,
use the combined gas law to find how the volume
reacts:
PV = P V 
Tk
Tk 
Pressure is measured in many ways:
760 mm Hg = 1 atm = Standard Pressure
When 2.00 L of a gas at STP is heated to 80.0˚C it
expands to a volume of 2.50 L. How must the
pressure have also changed?
V = 2.00 L
P  = PVTk 
T = 273˚K
TkV 
P = 760 mm Hg
T  = 353˚K
=(760 mm)(2.00 L)(353˚K)
V  = 2.50 L
∆P = ?
(273˚K)(2.50 L)
786 mm
∆P = P - P = 786 mm - 760 mm = 26 mm Hg
1) A certain gas occupies 3.00 L at 10.0˚C and
778 mm Hg. What volume will it occupy when
the temperature is raised to 100.0˚C and the
pressure is lowered to 750 mm Hg?
2) The density of air is 1.29 g/L at STP. What
will the density of air be at 50.0˚C and a pressure
of 1.23 atm?
3) If a gas will occupy 2.00 L at 25.0 ˚C and 775
mm Hg, what temperature change will bring it to
1.90 L if the pressure drops to standard?
1) A steel gas tank is filled to the brim with 56.0
L of gasoline on a day when the air temperature
is 5.0 ˚C. The car is then immediately placed in
garage where the temperature is 22.0˚C. How
much gas will spill out of the tank?
2) A washer has a 2.000 cm hole in it at room
temperature (20.0˚C). When it is plunged into
boiling water the diameter is 2.003 cm. What is
the washer made of?
3) One mole of a gas will occupy 22.4 L at
STP. What volume will one mole of hydrogen
occupy at -35.0˚C and 185.0 kPa?
A plumber wants to fit a copper ( = 16.8 X 10-6/
˚C) ring onto a pipe that is 4.000 cm in diameter.
The hole in the ring is only 3.980 cm. The ring and
the pipe are at room temperature (20.00˚C). To
what temperature must the plumber heat the ring in
order to get it to just slip over the pipe?
A large, calibrated Pyrex ( = 3 X 10-6/˚C) beaker
is filled with 1000.0 cm3 of water ( = 210 X 106/˚C) at 20.00˚C. If the flask and water are then
heated to 95.00˚C, what will the new reading be?