advertisement

Essential Physics II 英語で物理学の エッセンス II Lecture 2: 5-10-15 Course name student clicker ID ID Keitaro 02341011 1B3ED9 Jin Remember your clicker number! e.g. B12 (same every week) News Next lecture: Thursday 2015 / 10 / 15 (１０月１５日木曜日) This week’s homework: Also due: 2015/ 10 / 15 (１０月１５日) on http://masteringphysics.com News Homework: http://masteringphysics.com Use your student access code (with textbook) to login Join course EP22015TASKER News First time using MasteringPhysics? Do this introduction EVERYONE do this week’s homework News 6 problems News How do I use MasteringPhysics? Course website: http://astro3.sci.hokudai.ac.jp/ ~tasker/teaching/ep2/ Guide to registering or email me! [email protected] Homework = 40% of course mark! Pass mark = 60 % News How do I use MasteringPhysics? Course website: http://astro3.sci.hokudai.ac.jp/ ~tasker/teaching/ep2/ NO HOMEWORK =Guide FAIL COURSE! to registering or email me! [email protected] Homework = 40% of course mark! Pass mark = 60 % Last semester: Energy conservation Frictionless track Potential Energy Potential Energy Kinetic Energy Total energy is unchanged conversion Kinetic Energy Last semester: Energy conservation Friction track Potential Energy Potential Energy + Thermal Energy Kinetic Energy + Thermal Energy Total energy is unchanged conversion Kinetic Energy + Thermal Energy Thermal to mechanical energy Most of our energy is from heat: heat from burning fuel conversion mechanical energy Thermal to mechanical energy Most of our energy is from heat: heat from the sun conversion mechanical energy Can we convert 100% of heat energy to mechanical energy? No! Laws of thermodynamics This lecture ... ... studies thermal (heat) energy What is thermal equilibrium? Meaning of heat and temperature (and the difference between them) How temperature is measured How to use heat capacity to find equilibrium temperatures The 3 methods of heat transfer Thermodynamics = macroscopic macroscopic and mass kinetic energy microscopic mass kinetic energy macroscopic only pressure temperature depends on motion of all molecules pressure temperature Thermodynamic equilibrium You remove a cold drink from the refrigerator. Its temperature : (A) Stays the same (B) Changes to room temperature (C) Changes to hotter than room temperature (D) Stays colder than room temperature Quiz Thermodynamic equilibrium 6 C 26 C When drink = room temperature: temperature stops changing thermodynamic equilibrium 26 C 26 C When 2 systems are placed together and macroscopic properties do not change Cold Hot pressure length volume Thermodynamic equilibrium Quiz 2 blocks are placed together. 1 block expands (volume increase) but its pressure stays constant Was it in thermodynamic equilibrium? (A) No (B) Yes (C) Can’t know If ANY macroscopic property changes, they were not in thermodynamic equilibrium Thermodynamic equilibrium “Placed together” object #1 in thermal contact object #2 Heating object #1 changes macroscopic properties (e.g. pressure) of object #2 Thermodynamic equilibrium “Placed together” object #1 in thermal contact object #2 Heating object #1 changes macroscopic properties (e.g. pressure) of object #2 Not in thermal contact object #2 ‘s properties are unchanged Thermodynamic equilibrium A B C Thermodynamic equilibrium A If “A” is in thermal contact (and thermodynamic equilibrium) with “B” B C Thermodynamic equilibrium A If “A” is in thermal contact (and thermodynamic equilibrium) with “B” B C And “C” is in thermal contact (and thermodynamic equilibrium) with “B” Then “A” and “C” are in thermodynamic equilibrium (but not in contact) Thermodynamic equilibrium The zeroth (0th) law of thermodynamics: 2 systems in equilibrium with a 3rd system are in equilibrium with each other. A B C Thermodynamic equilibrium The zeroth (0th) law of thermodynamics: 2 systems in equilibrium with a 3rd system are in equilibrium with each other. A B C (If “A” is in equilibrium with “B” Thermodynamic equilibrium The zeroth (0th) law of thermodynamics: 2 systems in equilibrium with a 3rd system are in equilibrium with each other. A B C (If “A” is in equilibrium with “B” and “C” is in equilibrium with “B” Thermodynamic equilibrium The zeroth (0th) law of thermodynamics: 2 systems in equilibrium with a 3rd system are in equilibrium with each other. A B C (If “A” is in equilibrium with “B” and “C” is in equilibrium with “B” then “A” is in equilibrium with “C” ) Thermometer What is temperature? 2 systems have the same temperature if they are in thermodynamic equilibrium. A B thermal contact Same temperature measure temperature difference Thermodynamic equilibrium No macroscopic changes measure macroscopic change… Thermometer A system with a macroscopic property that changes with temperature height of mercury (Hg) gas pressure electrical resistance bending of bimetal (2 metals) strip The gas thermometer Constant-volume gas thermometer The gas thermometer Constant-volume gas thermometer Gas reaches thermodynamic equilibrium with system Pressure changes P The gas thermometer Constant-volume gas thermometer Gas reaches thermodynamic equilibrium with system P tube is moved to +/- atmospheric pressure Pressure changes ... so level is constant ‘h’ measures change in gas pressure and therefore, temperature The gas thermometer Need a temperature scale: Define 2 points: ‘0’ temperature = gas pressure is 0 0K Triple point for water: solid, liquid & gas water exist together 273.16 K (see next lecture) Since pressure cannot be < 0, 0 K = absolute zero can’t go lower! kelvin (K) SI unit Temperature scales Celsius 2 points: C T in F Rankine R 0 C Boiling point 100 C (standard atmospheric P) C = TC = T Fahrenheit melting point of ice T in K 273.15 in F 6= T in K 9 TF = TC + 32 5 T T in R = 0 R = 0K T in F 6= T in K Temperature scales Quiz When do the temperatures in centigrade and fahrenheit agree? (A) Never 9 TF = TC + 32 5 (B) At 0 degrees TF = TC (C) At 100 degrees 9 T = T + 32 5 (D) At -40 degrees T = (E) At -215 degrees 40 Energy How does a system reach thermodynamical equilibrium? ... T changes Why? because energy is moving. Heat is energy moving because of a difference in temperature ( T ) Temperature change T Energy change E Eheat Heat increases internal energy Heat capacity Heat energy transferred Eheat = Q [J] Q / = Temperature change T [K] C T heat capacity Q = mc depends on mass + material T specific heat capacity [J/kg · K] depends on what object is made of ... not how large it is Heat capacity Q = mc T Mass, m Specific heat, c Temperature, T Temperature increase, T Add energy E heat Q Q = mc T Heat capacity Old units for heat 1 calorie: heat needed to raise T of 1g of water from 14.5 C to 15.5 C = 4.184 J Heat capacity Quiz The mass of an object is 199.0 g It takes 16.0 J to raise the temperature by 10.0 C What is the specific heat? (A) 8.04 J/kg · K Q = mc T (B) 1600 J/kg · K Q c= m T (C) 0.00120 J/kg · K (D) 3.18 ⇥ 106 J/kg · K 16.0 = 0.199 ⇥ 10 Heat capacity Quiz A 905 g meteor hits the Earth at a speed of 1629 m/s If all the energy is converted to heat in the meteor, what is the temperature rise? specific heat of meteor: 472 J/kg · K (A) 2810 C (B) 2, 540, 000 C (C) 3.10 C (D) 11, 700 C 1 2 KE = mv Initial kinetic energy: 2 1 2 = 1, 200, 773 J = (0.905)(1629) 2 = heat energy = 1, 200, 773 T = 0.905 ⇥ 472 Q = mc T Equilibrium Temperature When 2 objects are in thermal contact, heat flows from the hotter to the colder object Eheat If objects are thermally insulated from the outside (no energy in or out) .... ... all energy leaving hotter object ends up in the colder object. m1 c1 T1 + m2 c2 T2 = 0 negative for hotter object E E Equilibrium Temperature Ex. An aluminum frying pan of mass 1.5 kg is at 180 C. It is dropped into 8 kg of water at 20 C. Assuming water does not boil and no heat is lost, what is the equilibrium temperature of pan and water? cp = 900 J/kg · K mp cp T + mw cw T = 0 mp cp (T Tp ) + mw cw (T Tw ) = 0 cw = 4184 J/kg · K equilibrium temperature mp cp Tp + mw cw Tw T = mp cp + mw cw 1.5 ⇥ 900 ⇥ 180 + 8.0 ⇥ 4184 ⇥ 20 = 1.5 ⇥ 900 + 8.0 ⇥ 4184 = 26 C Equilibrium Temperature Quiz A hot rock with mass 250 g is dropped into an equal mass of water. Which temperature changes more? (specific heat of water > rock) (A) rock (B) water mcr Tr + mcw Tw = 0 c r Tr = since: cr < cw Tr > (C) their temperature change is equal c w Tw Tw Heat Transfer Eheat HOW is heat transferred? 3 mechanisms: Conduction Convection Radiation Heat Transfer: Conduction Conduction: heat transfer from contact molecules in a hot region have more energy Heat Transfer: Conduction Conduction: heat transfer from contact molecules in a hot region have more energy collide with cold molecules Heat Transfer: Conduction Conduction: heat transfer from contact molecules in a hot region have more energy collide with cold molecules and transfer energy Heat Transfer: Conduction Conduction: heat transfer from contact How quick is the energy transfer? Depends the material’s thermal conductivity, k molecules in a hot region have more energy collide with cold molecules and transfer energy Heat Transfer: Conduction metals are good thermal conductors: contain free electrons that move fast Styrofoam is an insulator because it traps air. Heat Transfer: Conduction Heat flow depends on... THot T+ T A TCold x T thermal conductivity, k area, A thickness, Eheat = Q x temperature difference, Conductive heat flow: H= dQ dt rate of heat flow [W] T kA x T dT dx when area is not constant Heat Transfer Ex. What is the rate of heat conduction through the lake? Water thermal conductivity: k = 0.61 W/m · K H= T kA x = 30 C 4.0 C (0.61 W/m · K)(1.5 ⇥ 10 m ) 8.0 m = 3.0 MW 6 2 Heat Transfer 6 C 18 C 30 cm Quiz A solid concrete wall with area 4.0 m x 2.4 m Thermal conductivity, k = 1.3 W/m · K How much heat flow through the wall in 1 hour? (A) 1.8 MJ (B) 1.8 kJ (C) 500 J T H = kA x 6 C 18 C = (1.3 W/m · K)(4.0 m ⇥ 2.4 m) 0.3 m dQ = 499.2 W = dt (D) 5.0 MJ Q = 499.2 W ⇥ 3600 s = 1.8 MJ Heat Transfer: Conduction What if heat flows through different materials? The heat flow rate, H, must be the same through each material.... H H ... or it would collect between them Therefore... Heat Transfer: Conduction H= k1 A T2 T1 x1 x R= kA Define: = k2 A T3 T2 x2 Thermal resistance [K/W] Property of material and geometry (shape) H= T2 T1 R1 = T3 T2 R2 Heat Transfer: Conduction From: H= T2 T1 R1 = So: R1 H = T1 Adding: (R1 + R2 )H = T1 T3 T2 R2 T2 & R2 H = T2 = T1 T2 + T2 T3 T3 T3 T1 T3 H= R1 + R 2 Composite slab acts like a single slab with R = R1 + R2. Heat Transfer Quiz 3 slabs: Same area, A, and same thickness, x. Different thermal conductivities, k Which has the greatest temperature difference between its faces? (A) T1 (B) T2 (C) T3 H= T1 = R1 T1 (k) = T1 = R2 T2 (3k) = T1 = 3 T2 = 2 T3 T1 R3 T (2k) Heat Transfer: Convection Convection: heat transfer by fluid motion Heated fluid becomes less dense and rises It cools and sinks Heats again and rises Heat Transfer: Convection Heat Transfer: Radiation How do you feel heat from a stove? .... or the sun? .... or a lightbulb? Electromagnetic waves or radiation Heat Transfer: Radiation P = ✏ AT Stefan-Boltzmann law 4 = 5.67 ⇥ 10 object temperature 8 W/m2 · K4 emissivity: between 0 - 1, measures ability to emit radiation object emit radiation but.... ... they also absorb radiation Rate of absorption: P = ✏ ATa4 4 P = ✏ A(T Net radiated power: Ignore if object T >> background T : background temperature Ta4 ) sun = ignore human body = important Heat Transfer: Radiation P = ✏ AT P / T4 4 At high T, radiation is dominant heat loss mechanism ... at low T, radiation is less important In a vacuum (e.g. space) : only radiation [conduction & convection need a material (e.g. air) to transfer heat] Ex. Heat Transfer: Radiation e.g. The Sun A perfect emitter : ✏ = 1 blackbody (and absorber) T =? R 26 The Sun radiates energy at the rate P = 3.9 ⇥ 10 W 8 and its radius is 7.0 ⇥ 10 m . What is its surface T? ✓ ◆1/4 P 4 T = P = ✏ AT 2 4⇡R A = 4⇡R2 ✏=1 26 3.9 ⇥ 10 W = 4⇡(7.0 ⇥ 108 m)2 (5.7 ⇥ 10 8 W/m2 · K4 ) 3 = 5.8 ⇥ 10 K 1/4 Heat Transfer: Radiation Betelgeuse is a red super giant star Radiates heat at the rate of 2.70 ⇥ 10 30 W Surface T = 3000 K Assuming it is a perfect emitter ( ✏ = 1 ), what is the radius? = 5.67 ⇥ 10 8 (A) 7.80 ⇥ 10 11 2 W/m · K 4 m (C) 1.90 ⇥ 1011 m (B) 8.70 ⇥ 1011 m (D) 2.16 ⇥ 1011 m Quiz Quiz Heat Transfer: Radiation Betelgeuse is a red super giant star Radiates heat at the rate of 2.70 ⇥ 10 30 W Surface T = 3000 K Assuming it is a perfect emitter ( ✏ = 1 ), what is the radius? P = ✏ AT 4 P A= T4 P 4⇡R = T4 2 R= s R= r P 4⇡ T 4 (2.70 ⇥ 1030 W) 4⇡(5.67 ⇥ 10 8 W/m2 · K4 )(3000 K)4 = 2.16 ⇥ 10 11 m Heat Transfer What is the dominant (main) form of heat transfer from a red-hot stove burner with nothing on it. (A) conduction (B) convection (C) radiation (D) insulation Quiz Heat Transfer What is the dominant (main) form of heat transfer from a red-hot stove burner to a pot. (A) conduction (B) convection (C) radiation (D) insulation Quiz Heat Transfer What is the dominant (main) form of heat transfer from the bottom to the top of a pot containing boiling water. (A) conduction (B) convection (C) radiation (D) insulation Quiz Thermal - Energy Balance You home is warm in winter ... ... but it is losing energy heat loss Heat loss Eout / Tin / Tout Ein T House stays warm if: Eout Tin Tout heat loss rate = heat in rate dEout dEin = dt dt Thermal - Energy Balance Ex. A water heater loses heat at a rate of 120 W for each Celsius degree difference between the water and outside. dEout = (120 W/ C)( T ) dt T = Tin Tout It is heated by a 2.5 kW heater and the outside T = 15 C What is the water temperature? dEout dEin Thermo-energy balance: = dt dt 3 (120 W/ C)( T ) = 2.5 ⇥ 10 W Tin = 21 C + 15 C = 36 C T = 21 C