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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 .

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Thermal Expansion

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  1. Thermal Expansion the expansion or contraction of objects due to heat in or out Generally speaking: Heat in > expansion! Heat out > contraction!

  2. 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

  3. 100˚C 20˚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!

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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  =

  9. 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

  10. 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

  11. 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  =

  12. Sample Coefficients of Volume Expansion

  13. 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∆T 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 acetone =1490 X 10-6/˚C ∆T = 40.0 ˚C

  14. 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.

  15. 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).

  16. 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.

  17. 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!

  18. 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

  19. 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

  20. 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?

  21. 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?

  22. 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?

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