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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 .

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thermal expansion

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



  • 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 …..


Because God is not a DUMBASS!

if HE were like you:

because he is NOT:





expands !



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 ()




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


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 = • l∆T

l = 5.000 m

=(25 X 10-6/˚C)(5.000 m)(80.0˚C)

Ti = 20.0˚C

= .0100 m

l = ?

Tf = 100.0˚C

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 ()




per ˚C

 =


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


V = 2.119 L

Ti = 25.0 ˚C

= .119 L

(2.000 L)(40.0˚C)

Tf = 65.0 ˚C

 = ?

1.49 X 10-3 /˚C

∆V = .119 L


=1490 X 10-6/˚C

∆T = 40.0 ˚C


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 tank 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 (α = 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.


V = V

Tk Tk

Charles Law:

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!


PV = P V

Boyle’s Law:

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 

TkV 

T = 273˚K

P = 760 mm Hg

T  = 353˚K

=(760 mm)(2.00 L)(353˚K)

(273˚K)(2.50 L)

V  = 2.50 L

∆P = ?

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 10-6/˚C) at 20.00˚C. If the flask and water are then heated to 95.00˚C, what will the new reading be?