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Heat Transfer: Conduction • Hot Molecules Have More KE Than Cold Molecules

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Heat Transfer: Conduction • Hot Molecules Have More KE Than Cold Molecules PHYSICS 149: Lecture 26 • Chapter 14: Heat – 14.1 Internal Energy – 14.2 Heat – 14.3 Heat Capacity and Specific Heat – 14.5 Phase Transitions – 14.6 Thermal Conduction – 14.7 Thermal Convection – 14.8 Thermal Radiation Lecture 26 Purdue University, Physics 149 1 Final Exam • Wednesday, December 15, 8:00 – 10:00 AM • Place: MSEE B012 • Chapters 1 – 15 (only the sections we covered) • The exam is closed book. • The exam is a multiple-choice test. • There will be 30 multiple-choice problems. – Each problem is worth 10 points. • You may make a single crib sheet. – you may write on both sides of an 8.5” × 11.0” sheet. • Review session on Monday • Course Evaluation: – courseval.itap.purdue.edu/etw/ets/et.asp?nxappid=WCQ&nxmid=start&s=8 – open until 12/12/2010 Lecture 10 Purdue University, Physics 149 2 ILQ 1 The intensity of a sound wave is directly proportional to A) the frequency B) the square of the speed of sound C) the amplitude D) the square of the amplitude Lecture 26 Purdue University, Physics 149 3 ILQ 2 An open pipe (open at both ends) has a length of 50 cm. What is the wavelength of the second harmonic frequency? A) 25 cm B) 50 cm C) 75 cm D) 100 cm Lecture 26 Purdue University, Physics 149 4 Internal Energy • The internal energy of a system is the total energy of all of the molecules in the system except for the macroscopic kinetic energy (kinetic energy associated with macroscopic translation or rotation) and the external potential energy (energy due to external interactions). • Internal energy includes – Translational kinetic energy of the molecules • the average translational kinetic energy of the molecules of an ideal gas <Ktr> = (3/2)⋅k⋅TSI (Note: TSI in K) – Rotational and vibrational kinetic energy of the molecules – Potential energy between molecules – Chemical and nuclear binding energy of the molecules • Internal energy does not include – any energy related to outside or macroscopic sources or motions, like • overall translational energy of the system • potential energy due to external fields such as gravity. Lecture 26 Purdue University, Physics 149 5 Energy Conversion: Joule’s Experiment As the two masses fall, they cause paddles to rotate. – Gravitational potential energy is converted into kinetic energy of the paddle wheel. As the paddles agitate the water, it causes water’s temperature rise. – Kinetic energy of the paddle wheel is converted into internal energy. Lecture 26 Purdue University, Physics 149 6 Heat • Definition: Flow of energy between two objects due to difference in temperature – Note: similar to WORK – Object does not “have” heat (it has energy) • Units: calorie – Amount of heat needed to raise 1g of water 1ºC – 1 Calorie = 1 kcal = 1000 cal = 4186 Joules • Heat flows from a system at higher temperature to one at lower temperature Lecture 26 Purdue University, Physics 149 7 The Cause of Thermal Expansion • Objects expand when their temperatures increase because the vibrational energy of their molecules increases; this makes the average distance between molecules increase. – Example: liquid-in-glass thermometer relies on thermal expansion of the mercury or alcohol. Lecture 26 Purdue University, Physics 149 8 Thermal Expansion • When temperature rises – molecules have more kinetic energy • they are moving faster, on the average – consequently, things tend to expand • Amount of expansion depends on… – change in temperature Temp: T L – original length 0 Temp: T+ΔT – coefficient of thermal expansion ΔL •L0 + ΔL = L0 + α L0 ΔT • ΔL = α L0 ΔT (linear expansion) • ΔA = 2α A0 ΔT (area expansion) • ΔV = β V0 ΔT (volume expansion) Lecture 26 Purdue University, Physics 149 9 Expansion Coefficients Lecture 26 Purdue University, Physics 149 10 Thermal Expansion Lecture 26 Purdue University, Physics 149 11 Amazing Water Water is very unusual in that it has a maximum density at 4 degrees C. That is why ice floats, and we exist! ρ (kg m-3) T (C) Lecture 26 Purdue University, Physics 149 12 Stuck Lid ILQ A glass jar (α = 3x10-6 K-1) has a metal lid (α = 16x10-6 K-1) which is stuck. If you heat them by placing them in hot water, the lid will be A) Easier to open B) Harder to open C) Same Copper lid expands more, making a looser fit, and easier to open! Lecture 26 Purdue University, Physics 149 13 Jar ILQ A cylindrical glass container (β = 28x10-6 k-1) is filled to the brim with water (β = 208x10-6 k-1). If the cup and water are heated 50C what will happen? A) Some water overflows B) Same C) Water below rim Water expands more than container, so it overflows. Lecture 26 Purdue University, Physics 149 14 Heat Capacity, C • If no mechanical work is done either on or by a system, its change in internal energy is equal to the heat energy transferred into the system. • For many substances, the change in temperature is proportional to the change in heat energy; the constant of proportionality is called the heat capacity. In other words, the heat capacity of the system is the ratio of heat flow into a system to the temperature change of the system: – Heat capacity depends on both the substance and also on the amount of the substance which is present. – Heat capacity is a scalar quantity. – Units: J/K or J/˚C – Q > 0 for heat flow into the system, which causes ΔT > 0 – Q < 0 for heat flow out of the system, which causes ΔT < 0 Lecture 26 Purdue University, Physics 149 15 Specific Heat, c • The specific heat capacity (or specific heat) of a substance is the heat capacity per unit mass. – Specific heat means the amount of heat necessary to change the temperature of 1 kg of a substance by 1˚C – Specific heat depends only on the substance (since we divide the heat capacity by the mass). – Specific heat is a scalar quantity. – Units: J/(kg⋅K) or J/(kg⋅˚C) • If more than two substances are in contact, heat energy is transferred until they are all in thermal equilibrium. The final temperature and the changes in temperature of the various substances depend on the specific heats and the amounts of the substances that are present. • The heat required to produce a temperature change in a system is: – Q > 0 for heat flow into the system, which causes ΔT > 0 – Q < 0 for heat flow out of the system, which causes ΔT < 0 Lecture 26 Purdue University, Physics 149 16 Specific Heat • Heat adds energy to object/system • IF system does NO work then: – Heat increases internal energy: Q = ΔU – Heat increases temperature: Q = C ΔT •Q = c m ΔT – Heat required to increase T depends on amount of material (m) and type of material (c) •Q= cmΔT: “Cause” = “inertia” x “effect” (just like F=ma) – cause = Q – effect = ΔT – inertia = cm (mass x specific heat capacity) – c … specific heat • ΔT = Q/cm (just like a = F/m) Lecture 26 Purdue University, Physics 149 17 Phase Transitions • Phase transitions occur when a substance goes from one phase (solid, liquid, or gas) to another. • Phase transitions occur at constant temperature. During a phase transition, heat flow continues, but the temperature of the substance does not change. • The latent heat is the heat energy required per unit mass of effect a phase change. – The latent heat of fusion Lf: The heat per unit mass that must flow to melt a solid or to freeze a liquid (that is, Lf is for the solid-liquid transition). – The latent heat of vaporization Lv: The heat per unit mass that must flow to change the phase from liquid to gas or from gas to liquid (that is, Lv is for the liquid-gas transition). – Latent heat is a scalar quantity. – Unit: J/kg • Phase transitions can go in either direction, the latent heat is the same (but the heat energy flows the opposite way, of course). Lecture 26 Purdue University, Physics 149 18 Example: Ice Æ Water Æ Steam Phase Transitions m = 1 kg Q = miceciceΔT = 1 kg × 2.1 kJ/kg⋅K × 25 K = 52.3 kJ Q = mi+wLf = 1 kg × 333.7 kJ/kg = 333.7 kJ Q = mwatercwaterΔT = 1 × 4.19 × 100 = 419 kJ Q = mw+sLv = 1 × 2256 = 2256 kJ Q = msteamcsteamΔT = 1 × 2 × 25 = 50 kJ Lecture 26 Purdue University, Physics 149 19 Evaporation • Liquids evaporate due to the spread in kinetic energy of their molecules; the highest-energy molecules are able to escape (because it can break loose from the molecular bonds at the surface of the water), which reduces the average energy of those that are left (thereby cooling the liquid). Lecture 26 Purdue University, Physics 149 20 Molecular Picture of Gas • Gas is made up of many individual molecules • Number density is number of molecules/volume – N/V = ρ/m – ρ is the mass density – m is the mass for one molecule • Number of moles n = N / NA 23 -1 –NA = Avogadro’s number = 6.022×10 mole –NA= number of molecules per mole – 1 mole = amount of substance that contains as many elementary entities as there are atoms in exactly 12 grams of carbon-12 Lecture 26 Purdue University, Physics 149 21 Atoms, Molecules and Moles 23 • 1 mole = 6.022 × 10 molecules (NA = Avogadro’s Number) •NA = Number of atoms or molecules that make a mass equal to the substance's atomic or molecular mass in grams. • 1 u = 1 atomic mass unit = (mass of 12C atom)/12 – Approximately # of neutrons + # of protons – Atomic weight W -27 • 1 u = 1.66 × 10 kg = 1gram/NA • Mass of 1 mole of “stuff” in grams = molecular mass in u – E.g.
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