Lectures on Heat and Thermodynamics Physics 152 Michael Fowler, University of Virginia 8/30/08 Contents HEAT...........................................................................................................................................................3 Feeling and seeing temperature changes.....................................................................................3 Classic Dramatic Uses of Temperature-Dependent Effects..........................................................4 The First Thermometer........................................................................................................................5 Newton’s Anonymous Table of Temperatures ...............................................................................7 Fahrenheit’s Excellent Thermometer ...............................................................................................7 Amontons’ Air Thermometer: Pressure Increases Linearly with Temperature .............................7 Thermal Equilibrium and the Zeroth Law of Thermodynamics......................................................8 Measuring Heat Flow: a Unit of Heat ...............................................................................................8 Specific Heats and Calorimetry .......................................................................................................9 A Connection With Atomic Theory ................................................................................................10 Latent Heat .......................................................................................................................................11 THERMAL EXPANSION AND THE GAS LAW.............................................................................................12 Coefficients of Expansion................................................................................................................12 Gas Pressure Increase with Temperature......................................................................................13 Finding a Natural Temperature Scale............................................................................................13 The Gas Law .....................................................................................................................................14 Avogadro’s Hypothesis....................................................................................................................15 EARLY ATTEMPTS TO UNDERSTAND THE NATURE OF HEAT .....................................................................16 When Heat Flows, What, Exactly is Flowing? ................................................................................16 Lavoisier’s Caloric Fluid Theory .......................................................................................................16 The Industrial Revolution and the Water Wheel ...........................................................................17 Measuring Power by Lifting.............................................................................................................18 Carnot’s Caloric Water Wheel .......................................................................................................18 How Efficient are these Machines? ...............................................................................................19 Count Rumford.................................................................................................................................20 Rumford’s Theory of Heat................................................................................................................22 THE DISCOVERY OF ENERGY CONSERVATION: MAYER AND JOULE ....................................................24 Robert Mayer and the Color of Blood...........................................................................................24 James Joule......................................................................................................................................26 But Who Was First: Mayer or Joule? ...............................................................................................27 The Emergence of Energy Conservation ......................................................................................27 KINETIC THEORY OF GASES: A BRIEF REVIEW.........................................................................................28 2 Bernoulli's Picture ..............................................................................................................................28 The Link between Molecular Energy and Pressure ......................................................................29 Maxwell finds the Velocity Distribution ..........................................................................................30 Velocity Space .................................................................................................................................31 Maxwell’s Symmetry Argument......................................................................................................32 What about Potential Energy?.......................................................................................................37 Degrees of Freedom and Equipartition of Energy .......................................................................39 Brownian Motion ..............................................................................................................................39 IDEAL GAS THERMODYNAMICS: SPECIFIC HEATS, ISOTHERMS, ADIABATS..........................................39 Introduction: the Ideal Gas Model, Heat, Work and Thermodynamics ....................................39 The Gas Specific Heats CV and CP.................................................................................................40 Tracking a Gas in the (P, V) Plane: Isotherms and Adiabats ......................................................42 Equation for an Adiabat .................................................................................................................44 HEAT ENGINES: THE CARNOT CYCLE .....................................................................................................46 The Ultimate in Fuel Efficiency ........................................................................................................46 Step 1: Isothermal Expansion ..........................................................................................................47 Step 2: Adiabatic Expansion...........................................................................................................48 Steps 3 and 4: Completing the Cycle ...........................................................................................49 Efficiency of the Carnot Engine .....................................................................................................51 THE LAWS OF THERMODYNAMICS AND LIMITS ON ENGINE EFFICIENCY.............................................53 The Laws of Thermodynamics.........................................................................................................53 How the Second Law Limits Engine Efficiency .............................................................................55 A NEW THERMODYNAMIC VARIABLE: ENTROPY ...................................................................................57 Introduction ......................................................................................................................................57 Heat Changes along Different Paths from a to c are Different! ................................................57 But Something Heat Related is the Same: Introducing Entropy.................................................59 Finding the Entropy Difference for an Ideal Gas..........................................................................61 Entropy in Irreversible Change: Heat Flow Without Work............................................................62 Entropy Change without Heat Flow: Opening a Divided Box....................................................62 The Third Law of Thermodynamics.................................................................................................64 ENTROPY AND THE KINETIC THEORY: THE MOLECULAR PICTURE ..........................................................64 Searching for a Molecular Description of Entropy.......................................................................64 Enter the Demon ..............................................................................................................................65 Boltzmann Makes the Breakthrough..............................................................................................66 Epitaph: S = k ln W............................................................................................................................68 But What Are the Units for Measuring W ? ....................................................................................68 A More Dynamic Picture .................................................................................................................68 The Removed Partition: What Are the Chances of the Gas Going Back?...............................69 Demon Fluctuations.........................................................................................................................70 Entropy and “Disorder”....................................................................................................................71