Thermal Expansion

•the expansion or contraction of objects due to heat in or out

•Generally speaking:

•Heat in > expansion!

•Heat out > contraction!

Thermal ExpansionThermal 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 changeoriginal size

Because God is not a DUMBASS!

A notable exception to the rule of thermal expansion is …..

WATER

if HE were like you: because he is NOT:water:

100˚C

4˚C

contracts

0˚C

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 ()

= ∆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 α (C˚) -1

Aluminum 25 x 10-6

Brass 19 x 10 -6

Iron (steel) 12 x 10 -6

Glass (Pyrex) 3 x 10-6

Glass (ordinary) 9 x 10 -6

Quartz 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

Tf = 100.0˚Cl = ?

∆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

MATERIAL β (C˚) -1

Gasoline 950 x 10-6

Acetone 1500 x 10-6

Mercury 180 x 10-6

Ethyl Alcohol 1100 x 10-6

Glycerin 500 x 10-6

Water 210 x 10-6

Sample Coefficients of Volume Expansion

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/˚Cacetone

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 TkCharles 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!

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 LT = 273˚KP = 760 mm HgT = 353˚K

V = 2.50 L

∆P = ?

P = PVTk

TkV =(760 mm)(2.00 L)(353˚K)

(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 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?

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?