Energy and Entropy Physics 423 David Roundy Spring 2012 Draft 1/30/2012 Contents Contents i 1 Monday: What kind of beast is it?1 1.1 Thermodynamic variables (Chapter 1 ).......... 1 Activity: Thermodynamic variable cards (4 min) ............... 1 Required homework 1.1: steam-tables.................. 2 Activity: Dimensions (5 min?) .......................... 2 Activity: Conjugate pairs (10 min?) ...................... 2 Activity: Intensive vs. extensive (10-15 min) .................. 2 Required homework 1.2: extensive-internal-energy........... 2 Activity: State variables and functions (5 min?) ................ 2 Activity: Conserved quantities (??? min) .................... 3 Thermodynamic equilibrium ............. 3 Lecture: (??? min) ................................ 3 Equations of state ............... 3 Lecture: (3-4 min) ................................ 3 Physics 423 i 2 Tuesday: 4 Activity: Math pretest (15 min) ......................... 4 2.1 Partial derivatives as change of variables .........4 Lecture: (???) ................................... 4 Activity: Paramagnetism (??? min) ...................... 4 Activity: Ideal gas bulk modulus (??? min) .................. 4 2.2 Total differential ................ 5 Lecture: (11 min) ................................. 5 BWBQ: (5 min) ................................. 6 Lecture: (5 min) ................................. 6 BWBQ: (15 min) ................................. 6 Exact vs. inexact differentials ............ 7 BWBQ: (10 min) ................................. 7 Lecture: (5 min?) ................................. 7 Required homework 1.3: total-differentials............... 7 2.3 Chain rules ................. 7 Lecture: (10 min) ................................. 7 Exam: Math pretest ........................... 8 Question 1 .................................... 9 Question 2 .................................... 9 Question 3 .................................... 10 Question 4 .................................... 11 3 Wednesday: 12 Handout: Changes of variables...................... 12 Homework 1 due ................................. 14 Problem 1.1 Steam tables ............................ 14 Problem 1.2 Extensive internal energy ..................... 14 Problem 1.3 Total differentials ......................... 14 4 Thursday: 15 4.1 Mixed partial derivatives ..............15 Activity: BWBQ: Mixed partials (30-40 min?) . 15 Activity: Mixed partials vanishing (??? min) . 15 Handout: Mixed partial derivatives................... 15 Required homework 2.1: a-maxwell-relation .............. 19 Required homework 2.2: adiabatic-susceptibility............ 19 Required homework 2.3: summation-notation ............. 19 Required homework 2.4: homogeneous-function-theorem . 19 Monotonicity and invertibility ............19 Activity: Monotonicity lecture/discussion (10 min) . 19 Legendre transform ...............20 Lecture: (??? min) ................................ 20 Physics 423 ii 5 Friday: Lagrange multipliers for minimization 23 Homework 2 due ................................. 23 Problem 2.1 A Maxwell relation ........................ 23 Problem 2.2 Adiabatic susceptibility ...................... 23 Problem 2.3 Summation notation........................ 24 Problem 2.4 Euler's homogeneous function theorem.............. 24 6 Monday: Lab 1: Heat and Temperature 26 Lecture: (10 min) ................................. 26 Activity: Energy/Heat equivalence (15 min now, 10 min later) . 26 SWBQ: (5 min) .................................. 26 SWBQ: (5 min) .................................. 26 SWBQ: (5 min) .................................. 26 Lecture: (10 min) ................................. 26 SWBQ: (5 min?) ................................. 27 Dulong-Petit Law ................27 Lecture: (5 min) ................................. 27 7 Tuesday: First and Second Laws 28 Activity: Name-the-experiment pretest (10 min) . 28 System and surroundings ..............28 Lecture: (2-3 min) ................................ 28 BWBQ: (10 min) ................................. 28 7.1 First Law ..................28 Lecture: (10 min) ................................. 28 SWBQ: (5 min) .................................. 29 7.2 Second Law and Entropy ..............29 SWBQ: (1 min) .................................. 29 Lecture: (5 min) ................................. 29 Fast and slow .................30 Lecture: (7-12 min) ................................ 30 7.3 The thermodynamic identity (5.1.2.2 ).......... 30 Lecture: (8-15 min) ................................ 30 Activity: Name the experiment (20 min) .................... 30 7.4 Heat capacity .................31 SWBQ: (5 min (skipped in 2011)) ........................ 31 Lecture: (10 min) ................................. 31 BWBQ: (10 min (skipped in 2011)) ....................... 32 Lecture: (5 min (skipped in 2011)) ....................... 32 Activity: Entropy change of cooling coffee (20-30 min (skipped 2010)) . 32 Required homework 3.1: adiabatic-ideal-gas .............. 33 Required homework 3.2: bottle-in-bottle................ 33 Exam: Pretest............................... 33 Physics 423 iii Question 1 .................................... 34 Question 2 .................................... 34 8 Wednesday: Second Law lab 35 Activity: Melting ice (45 min) .......................... 35 Lab 1 due..................................... 35 Question 1.1 Plot your data I .......................... 36 Question 1.2 Plot your data II.......................... 36 Question 1.3 Specific heat ............................ 37 Question 1.4 Latent heat of fusion........................ 37 Question 1.5 Entropy for a temperature change ................ 37 9 Thursday: Heat and work 38 Activity: Expanding Gas Quiz (20-45 min) ................... 38 Handout: Quiz .............................. 38 Question 1 Free expansion............................ 39 Activity: Name the experiment with changing entropy (20 min) . 40 9.1 Work ...................40 Lecture: (5 min) ................................. 40 BWBQ: (10 min) ................................. 40 Activity: Using pV plots (20-30 min) ...................... 40 Activity: Using TS plots (15-20 min) ...................... 41 Activity: Name the experiment for a rubber band (15 min) . 41 10 Friday: 42 10.1 Engines and Fridges ...............42 Other views of the Second Law ............42 Lecture: (??? min) ................................ 42 Carnot efficiency ................42 Lecture: (??? min) ................................ 42 Activity: Carnot efficiency (??? min) ...................... 44 Activity: Big money (15 min?) ......................... 44 Lab 2 due..................................... 45 Question 2.1 Mass of ice remaining ....................... 46 Question 2.2 Final temperature of water .................... 46 Question 2.3 Change in entropy of water.................... 46 Question 2.4 Change in entropy of ice...................... 47 Question 2.5 Net change............................. 47 Question 2.6 Mass of ice remaining ....................... 47 Question 2.7 Final temperature ......................... 47 Question 2.8 Errors? ............................... 47 Homework 3 due ................................. 48 Problem 3.1 Adiabatic compression....................... 48 Physics 423 iv Problem 3.2 A bottle in a bottle ........................ 48 Practice homework 4.1: power-from-ocean ............... 49 Required homework 4.2: power-plant-river............... 49 Required homework 4.3: heat-pump................... 49 11 Monday: 50 Monotonicity and invertibility ............50 Activity: Monotonicity lecture/discussion (10 min) . 50 11.1 Thermodynamic potentials (Chapter 7 ).......... 51 Legendre transform ...............51 Activity: Legendre transform revisited (15 min?) . 51 Activity: Understanding the potentials (20 min) . 52 Lecture: (5 min?) ................................. 52 Required homework 4.4: gibbs-free-energy ............... 53 11.2 Maxwell relations ................53 Lecture: (5 min) ................................. 53 BWBQ: (15-25 min) ............................... 53 Activity: Name the experiment with Maxwell relations (10 min) . 54 12 Tuesday: Lab 2: rubber band 55 Activity: Rubber band lab............................ 55 Prelab 3 due.................................... 55 Question 3.1 Tension vs. temperature...................... 56 Question 3.2 Isothermal stretch ......................... 56 Lecture: (10 min) ................................. 57 Required homework 4.5: free-expansion................. 58 13 Wednesday: 59 Activity: Name another experiment with Maxwell relations (10-20 min) . 59 Homework 4 due ................................. 59 Problem 4.1 Power from the ocean (practice).................. 59 Problem 4.2 Power plant on a river....................... 60 Problem 4.3 Heat pump ............................. 60 Problem 4.4 Using the Gibbs free energy.................... 61 Problem 4.5 Free expansion ........................... 61 14 Thursday: Thermodynamics practice 62 Activity: Simple cycle (40-110 min) ....................... 62 Activity: Temperature change of dissolving salt (40 min?) . 62 Activity: Never, sometimes or always true (60 min?) . 63 Handout: ................................. 63 15 Friday: Thermodynamics practice 66 Physics 423 v Activity: Black body thermodynamics (30 min) . 66 Activity: Applying the second law........................ 66 Required homework 5.1: maine-entropy-2nd-law-spontaneous-metal . 67 Required homework 5.2: isothermal-adiabatic-compressibility . 67 Lab 3 due....................................