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

3. 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

4. 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 =.5mv 2 ) therefore, if the temperature is changing, the speed of the molecules is changing!

5. 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

6. 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 H 2 O up 1 ˚C Since heat is a form of energy, it is measured in Physics in Joules 4.19 J = 1 cal

7. 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

8. 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 !

9. Thermal expansion of solids depends upon: original length-- l temperature change-- ∆T = T f - T i the rate at which the material will expand per ˚C per original length: the coefficient of linear expansion (  )  = ∆l l∆T units: per ˚C

10. 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  MATERIALα (C˚) -1 Aluminum25 x 10 -6 Brass19 x 10 -6 Iron (steel)12 x 10 -6 Glass (Pyrex)3 x 10 -6 Glass (ordinary)9 x 10 -6 Quartz0.4 x 10 -6

11. 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 T i = 20.0˚C T f = 100.0˚C l = ? ∆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

12. Thermal expansion of liquids depends upon: original volume-- V temperature change-- ∆T = T f - T i the rate at which the material will expand per ˚C per original volume: the coefficient of volume expansion (  )  = ∆V V∆T units: per ˚C

13. MATERIALβ (C˚) -1 Gasoline950 x 10 -6 Acetone1500 x 10 -6 Mercury180 x 10 -6 Ethyl Alcohol1100 x 10 -6 Glycerin500 x 10 -6 Water210 x 10 -6 Sample Coefficients of Volume Expansion

14. 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 T i = 25.0 ˚C T f = 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

15. 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.

16. A glass (α = 9 X 10 -6 /˚C) beaker that is 1000.0 cm 3 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).

17. 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.

18. V = V T k 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!

19. 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 T k T k Pressure is measured in many ways: 760 mm Hg = 1 atm = Standard Pressure

20. 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 T = 273˚K P = 760 mm Hg T = 353˚K V = 2.50 L ∆P = ? P = PVT k T k V =(760 mm)(2.00 L)(353˚K) (273˚K)(2.50 L) 786 mm ∆P = P - P = 786 mm - 760 mm = 26 mm Hg

21. 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?

22. 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?

23. A large, calibrated Pyrex (  = 3 X 10 -6 /˚C) beaker is filled with 1000.0 cm 3 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?