1. Physics 7A -- Lecture 2 Winter 2009 Prof. Robin D. Erbacher 343 Phy/Geo Bldg erbacher@physics.ucdavis.edu Prof. Robin D. Erbacher 343 Phy/Geo Bldg erbacher@physics.ucdavis.edu

2. Physics 7A -A/B This course has two instructors:  Prof. Robin Erbacher (me) rderbacher @ucdavis  Ruggero Tacchi (Lead DL Instructor) rtacchi @ucdavis You are enrolled in one of two 7A classes.  7A-C/D has lectures on Tuesdays.  We are independent courses but cover the same material, so you can attend any review session.  We have a common final exam. The final exam is Friday March 20 th, 6:00 pm-8:00 pm  If you know you cannot make the final, you should take 7A in a different quarter. There are no make-up exams. This course has two instructors:  Prof. Robin Erbacher (me) rderbacher @ucdavis  Ruggero Tacchi (Lead DL Instructor) rtacchi @ucdavis You are enrolled in one of two 7A classes.  7A-C/D has lectures on Tuesdays.  We are independent courses but cover the same material, so you can attend any review session.  We have a common final exam. The final exam is Friday March 20 th, 6:00 pm-8:00 pm  If you know you cannot make the final, you should take 7A in a different quarter. There are no make-up exams.

3. AnnouncementsAnnouncements Join this Class Session with your PRS clicker! (Practice run today, credit begins next time.) Quiz today! Lecture 1, DLM 1 + FNTs. Must take it in correct lecture time slot. Check Physics 7 website frequently for calendar & announcements. DL Instructors have PTA numbers for adding this class. No Lecture next week! Turn off cell phones and pagers during lecture.

4. Models in Physics 7A Three-phase model of matter Energy-interaction model Mass-spring oscillator Particle model of matter  Particle model of bond energy  Particle model of thermal energy Thermodynamics Ideal gas model Statistical model of thermodynamics We started with these two… We introduce this one next (chapter 2)

5. 3-Phase Model Revisited

6. Three Phase Model of Matter Solid: Keeps its shape without a container. Liquid: Takes the shape of the (bottom of) the container. Keeps its volume the same. Gas: Takes the shape and volume of the container. Example H 2 O

7. Graph of Ice to Steam T bp : Temperature at which a pure substance changes phase from liquid to gas (boiling point). T mp : Temperature at which a pure substance changes phase from solid to liquid (melting point). T bp T mp

8. Phase Changes - a recap You take ice out of the freezer at -30 0 C and place it in a sealed container and slowly heat it on the stove. You would find: the temperature of the ice rises, remains fixed at 0 0 C for an extended time while it is a mixture of ice and water, the temperature rises again after it all melted, remains fixed at 100 0 C for an extended time while it is a mixture of liquid and gas, the temperature rises again after it is all gas (steam).

9. Three Phase Model of Matter Q How do we change the phase of matter? How do we change the temperature of matter? A By adding or removing energy. In some cases this energy is transferred from, or to, the substance as heat, “Q”. Example H 2 O

10. Thermal Equilibrium and Heat

11. An ice-cube sits in a bath of water. Water and ice can exchange heat with each other but not with the environment. What is the direction of heat transfer? A. From ice-cube to water B. From water to ice-cube C. Neither of above D. Impossible to tell Heat Transfer 0 0 C Water Ice-cube 0 0 C

12. Thermal Heat Starting definition of heat (to be revised much later): Heat (Q) is the transfer of energy from a hot object to a cold object because the objects are at different temps. Corollary: If the two objects are at the same temperature, no Q (heat) flows between them. Energy leaves hot objects in the form of heat. Energy enters cold objects in the form of heat. Low temp High temp Q

13. EquilibriumEquilibrium The Zeroth law of thermodynamics says: Since they are in thermal equilibrium with each other, there is no net energy exchanged among them. If objects A and B are separately in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other If objects A and B are separately in thermal equilibrium with a third object C, then A and B are in thermal equilibrium with each other

14. Thermal Equilibrium If the two objects are at the same temperature, no heat flows between them. in thermal equilibrium A system in thermal equilibrium is a system whose temperature is not changing in time. T final Energy leaves hot objects in the form of heat Energy enters cold objects in the form of heat Low tempHigh temp

15. EquilibriumEquilibrium The Zeroth law of thermodynamics example: Let the third object C be the thermometer. If the two readings are the same, then A and B are also in thermal equilibrium. Energy (heat) will not flow between A and B if put together.

16. Reaching Thermal Equilibrium A cup of hot coffee left in a room… A thermometer Cold beer It can take some time for things to reach thermal equilibrium with its environment. ~ what is happening at microscopic level? => more to come when we cover Particle models of thermal energy

17. Slowing things down… C = [C] = J/K Coffee cup: ceramic material A thermometer Tip: metal Body: glass, plastic Beer glass: glass Heat capacity [C] of substances: A measure of the amount of energy required to increase the temperature of the substance a certain amount

18. Heat Capacity Heat capacity C is an extensive property: 2kg of water will have twice the heat capacity of 1kg water Heat capacity of substances: A measure of the amount of energy required to increase the temperature of the substance a certain amount C = [C] = J/K

19. Specific Heat Capacity Porcelain 1.1kJ/kgK Tip:metal (Silver: 0.24kJ/kgK) Body: plastic ~ 1.2kJ/kgK Glass 0.84kJ/kgK Specific heat capacity C p is an intensive property: Specific heat capacity only depends on the substance Specific heat capacity C p of substances: the amount of energy per unit mass/unit mole required to increase the temperature of the substance by one degree Kelvin [C p ] = kJ/kgK = kJ/moleK

20. An Aside on “calories” The scientific "calorie" is spelled with a lower-case "c". One "calorie" = 4.184 Joules The "dieter's" calorie is spelled with an upper-case "C". One "Calorie" = 1000 calories

21. Clicker Question You heat 1 L of water and raise its temperature by 10 0 C. (Water~1g/ml) Question: If you add the same quantity of heat to 2 L of water, how much will the temperature rise? a)Not enough information is given. b)Twice as much. c)Half as much.

22. Clicker Question You heat 1 L of water and raise its temperature by 10 0 C. (Water~1g/ml) Question: If you add the same quantity of heat to 5 L of water, how much will the temperature rise? a)Not enough information is given. b)2 0 C. c)50 0 C.

23. Heat capacity C – sort of the slope here of A, C, E Heat of fusion Heat of vaporization EE

24. Heat Capacity in the Three-phase Model of Matter Temperature (K) Energy added (J) solid liquid gas ∆T ∆E C = [C] = J/K

25. Heat Capacity in the Three-phase Model of Matter Temperature (K) Energy added (J) solid liquid gas TbTb ∆E C = [C] = J/K

26. Heat of Vaporization Temperature (K) Energy added (J) solid liquid gas TbTb ∆E “Heat” of vaporization : ∆H the amount of energy per unit mass/unit mole required for a substance to change its phase from liquid to gas or vice versa

27. Heat of Fusion Temperature (K) Energy added (J) solid liquid gas TmTm ∆E “Heat” of fusion (melting) : ∆H the amount of energy per unit mass/unit mole required for a substance to change its phase from solid to liquid or vice versa

28. Temperature (K) Energy added (J) solid liquid gas TmTm ∆E Typically, ∆H v >> ∆H m e.g. It takes 6 times more energy to vaporize 1kg of water than to melt the same amount of ice TbTb ∆E

29. Energy Change  E In our notation, we always have  E = E final - E initial.  E negative: Energy is released from the system. (“Neg. energy added.”)  E positive: Energy is put into the system.  Be sure to select the correct sign for all energy transfers! => Note also:  T is always T f - T i.

30. Definitions Review Heat capacity - Extensive -How much energy it takes to change the temperature of this amount of pure substance (see parts A, C and E in graph). Specific heat capacity (or specific heat) - Intrinsic -How much energy it takes to change the temperature per unit of pure substance (mass/mole) (parts A, C and E). Heat of fusion - Intrinsic -How much energy it takes to melt all of the ice to water (see isothermal part B of graph). Heat of vaporization - Intrinsic - How much energy it takes to boil all the water to steam (see isothermal part D of graph).

31. Clicker Question You put a red hot iron 1.0 kg mass into 1.0 L of cool water. 1)The increase in the water temperature is equal to the decrease in the iron’s temperature. True or False?

32. Clicker Question You put a red hot iron 1.0 kg mass into 1.0 L of cool water. 1) The increase in the water temperature is equal to the decrease in the iron’s temperature. True or False? 2) The iron and the water will both reach the same temperature. True or False?

33. Conservation of Energy and the Energy Interaction Model

34. Conservation of Energy Energy is a thing (quantity). You & I contain energy, as do the chairs you sit on and the air we breathe. We cannot see it, but we can measure the transformation of energy (or change,  E) through measuring a process. Conservation of Energy Energy cannot be created nor destroyed, simply converted from one form to another. Conservation of Energy Energy cannot be created nor destroyed, simply converted from one form to another. If the energy of an object increases, something else must have given that object its energy. If it decreases, it has given its energy to something else. A transfer of energy is when one object gives energy to another. There are 2 types of energy transfers  E -- Heat and Work.

35. Remember Particle Physics? Protons + anti-protons  New particles! Fermilab Conservation of Energy Energy cannot be created nor destroyed, simply converted from one form to another. E=Mc 2 ! x x

36. Energy Systems E therma l E bond E movement (KE) E gravit y E electri c E sprin g There are many different types of energies called energy systems:........ For each energy system, there is an indicator that tells us how that energy system can change: E thermal : indicator is temperature E bond : indicator is the mass of the initial and final phases

37. Energy System Expressions E thermal = C  T, Temperature is the indicator. Between phase changes, only thermal energy changes. E bond =  |  m  H|,  m is the indicator. At a physical phase change, only the bond-energy system changes.  H is the heat of the particular phase change.  m is the amount that changed phase. In a chemical reaction, there are several bond energy changes corresponding to diff. molecular species (reactants or products). Here  H is the heat of formation for a particular species. E therma l E bond

38. Energy Interaction Diagrams - Closed System EaEa EbEb EcEc Conservation of Energy The total energy of a closed physical system must remain constant. So, the change of the energies of all energy systems associated with the physical system must sum to zero. Change in closed system energy = ∆E a + ∆ E b + ∆ E c = 0

39. Energy Interaction Diagrams - Open System EaEa EbEb EcEc Conservation of Energy The change of the energies of all systems associated with an open physical system must sum to the net energy added or removed. Energy is added or removed as Heat or Work. Change in open system energy = ∆E a + ∆ E b + ∆ E c = (Energy added) - (Energy removed) = Q + W. Energy addedEnergy removed

40. Example for Open System E a Energy added = + 100 J Suppose we have a system where 100J of heat comes in from the outside. Joe claims that the only energy system that changes is E a and that  E a is negative (E a decreases). Can Joe be correct? 1)Yes, its possible that he is correct. 2)Yes, Joe is definitely correct. 3)No way is Joe’s description correct. Clicker!

41. Energy Interaction Diagrams Example: Melting Ice T i = 0°C  T f = room temperature Temperature Energy of substance solid liquid gas l-g coexist s-l coexist Initial T MP T BP Final

42. Energy Interaction Diagrams Example: Melting Ice Process 1: Ice at T=0ºC  Water at T=0ºC Process 2: Water at T=0ºC  Water at room temperature Temperature Energy of substance solid liquid gas l-g coexist s-l coexist Process 1 Initial T MP T BP Process 1 Final / Process 2 Initial Process 2 Final

43. Energy Interaction Diagrams Example: Melting Ice Process 1: Ice at T=0ºC  Water at T=0ºC Ice ∆T = 0 ∆E th = mC p  T = 0 Initial phase Solid, Final phase Liquid E therm al E bond

44. Energy Interaction Diagrams Example: Melting Ice Process 1: Ice at T=0ºC  Water at T=0ºC Ice ∆T=0 ∆E th = mC p  T =0 Initial phase Solid, Final phase Liquid E therm al E bond Heat

45. Energy Interaction Diagrams Example: Melting Ice Process 1: Ice at T=0ºC  Water at T=0ºC Ice Initial phase Solid, Final phase Liquid ∆E th + ∆E bond = Q+W ∆E bond = ±|  m||  H| = Q E therm al E bond Heat MwMw ∆T=0 ∆E th = mC p  T =0

46. Energy Interaction Diagrams Example: Melting Ice Process 2: Water at T=0ºC  Water at room temperature Ice Initial phase Liquid, Final phase Liquid E therm al E bond

47. Energy Interaction Diagrams Example: Melting Ice Process 2: Water at T=0ºC  Water at room temperature Ice Initial phase Liquid, Final phase Liquid ∆E bond = ±|  m||  H| = 0 E therm al E bond T Heat ∆E th + ∆E bond = Q+W ∆E th = mC p  T = Q

48. Energy Interaction Diagrams Example: Melting Ice Ice Initial phase Liquid, Final phase Solid E therm al E bond Freezing (Water at T=0°C  Ice at T=0°C) ∆T=0 ∆E th = mC p  T= 0 Heat NOTE: Heat is released when bonds are formed! (In general  E is negative) MwMw

49. EIM Algebra Review For a closed system: (Is it clear why there’s no Q or W for a closed system?) For an open system: (Q and W can be positive or negative, as can  Es.)

50. Next Time: Two New Energy Systems

51. Backup Information:

52. Energy Interaction Model Algebra Review Kelvin: the standard for scientific use. Increasing the temperature by 1 K = Increasing the temperature by 1 0 C Celsius/Centigrade Same as Kelvin except 0 in a different place Fahrenheit Smaller unit of temperature

53. Heat Capacity The heat capacity, C, of a particular substance is defined as the amount of energy needed to raise the temperature of that sample by 1° C. If energy (heat, Q) produces a change of temperature,  T, then: Heat capacity depends on the amount of a substance we have, since it will take more energy to change the temperature of a larger quantity of something. It is thus called an extensive quantity, or dependent upon the quantity/mass of a substance (kg or mole). Q = C  T

54. Specific Heat The specific heat capacity, often simply called specific heat, is a particular number for a given substance and does not depend on quantity. Specific heat is thus an intensive property. The specific heat of water is one calorie per gram per degree Celsius. The specific heat of water is one calorie per gram per degree Celsius. SI units for heat capacity and specific heat: heat capacity J/K specific heatJ/kgK, or J/molK (molar specific heat)