Thermal & Kinetic Philip Moriarty School of Physics & Astronomy B125, x 15156, philip.moriarty@nottingham LECTURE 1 OVERVIEW “Atoms and molecules in crowds” Module organisation + syllabus Teaching and assessment Forces and potentials Introduction to temperature and changes of phase Demonstration movie from “Matter & Interactions”, Ruth Chabay and Bruce Sherwood. © Ruth Chabay

“Why should I care about thermal and kinetic properties?” X “Why should I care about thermal and kinetic properties?” Thermodynamics is concerned with the macroscopic properties of a system (e.g. P, T, V). Developed in 19th century – classical physics - related to study of heat flow. However, modern physics tends to explain physical properties from a microscopic (indeed, nanoscopic) perspective – we can now routinely ‘see’ and move individual atoms and molecules. Link between microscopic......... P, T, V and macroscopic? Statistical mechanics Statistical mechanics is a fundamental, central and pervasive part of physics. It underlies our understanding of the collective behaviour of atoms in solids, liquids, gases. “More is different” (PW Anderson Science 177 393 (1972))

“Why should I care about thermal and kinetic properties?” X “Why should I care about thermal and kinetic properties?” Without statistical physics just a few of the things we wouldn’t understand are: why metals are stable solids; why Cu is a metal whereas diamond is an insulator; why certain materials are ferromagnetic; why different isotopes of the same element can behave so differently; At the end of the module you should be able to answer the following questions (amongst very many others!): why does energy not flow from low temperature to high temperature?; why aren’t perpetual motion machines possible?; why can’t I cool my kitchen down by leaving the ‘fridge door open?; why the “temperature of the Universe” is 3K; just what is entropy?

“How are kinetic processes and thermodynamics linked?” Best to think of this module as a study of “atoms and molecules in crowds”* Atomic and molecular interactions Kinetic theory – ideal and real gases How do thermodynamic laws and variables stem from atomistic/molecular picture of gases? Entropy: “..can I count the ways?” Thermal and kinetic properties of solids and liquids * “The Laws of Nature”, RE Peierls (1955)

Syllabus I. Atomic Interactions and Arrangements NOTE THAT SYLLABUS HAS BEEN MODIFIED SLIGHTLY SINCE THE START OF THE MODULE. IN PARTICULAR, COMPONENTS III AND IV HAVE BEEN SWAPPED AND SOME MATERIAL HAS BEEN DROPPED (PJM 15TH APRIL ’03) Syllabus I. Atomic Interactions and Arrangements Interatomic forces and potentials: bonding; intro. To temperature and changes of phase; vapour, vapour pressure and evaporation; latent heats II. Kinetic theory: Distributions, Energy and Heat Flow Distributions and the mathematics of averaging; the ideal gas law; ideal and real gases; van der Waals equation; Boltzmann factors; Maxwell-Boltzmann distribution; equipartition theorem, degrees of freedom, specific heats; blackbody radiation; diffusion, mean free path, viscosity; conduction, convection, radiation; III. Thermodynamics from micro- and macroscopic perspectives The 0th law, thermal equilibrium and thermometry; heat, energy, work and the 1st law; isothermal and adiabatic processes; PV diagrams; the ideal gas law revisited; phase diagrams, iostherms, and phase transitions; IV. Entropy and Probability Probability, disorder and the 2nd law; reversibility (and irreversibility); microstates and macrostates; entropy; engines and refrigerators; Carnot cycle; efficiencies;

Syllabus V. Thermal and Kinetic Properties of Solids and Liquids Specific heat; thermal expansion; heat conduction; lattice vibrations and Einstein’s model; radiant heat and limitations of kinetic theory;

Teaching, Assessment and the Web Lectures Printed lecture notes handed out. Goal is to encourage your active involvement (albeit difficult with ~ 140 students!). Read notes BEFORE lecture + attempt to answer questions in notes. Will also have sessions towards the end of the course dedicated to problems and past exam papers. Web www.nottingham.ac.uk/~ppzpjm

Teaching, Assessment and the Web 15% of module assessment based on coursework. (NB Some of the coursework will be computer-based). 85% of module assessment based on exam. 2 hour exam – standard format, (as for other core modules). Textbooks Printed notes handed out. However, do not rely on these alone. USE THE LIBRARY. Primary recommended textbook is Grant & Phillips (Chapters 12- 14). See Module Information booklet for list of secondary texts and websites.

Solids, Liquids and Gases: Forces and Potentials “If, in some cataclysm, all of scientific knowledge were to be destroyed and only one sentence [could be] passed onto the next generation of creatures, what statement would contain the most information in the fewest words?” “All things are made of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another” RP Feynman, “The Feynman Lectures in Physics”, Vol I (1963)

Solids, Liquids and Gases: Forces and Potentials Solid matter is comprised of interacting atoms and molecules – how might we model those interactions? Atom Interatomic bond (produces interaction force) Model the solid as set of balls and springs – use this model to examine distribution of energy in a solid…… Before going any further let’s revise motion of a mass on a spring. Assuming simple harmonic motion, the force exerted by the spring on the ball depends: linearly, quadratically, or exponentially on the displacement? ? ANS: (a), F = - kx (where x is the displacement). (Lots of SHO in Vibrations & Waves Module!)

Solids, Liquids and Gases: Forces and Potentials The force is given by F= - kx, therefore the potential energy is given by: (a) kx2, (b) k/x2, (c) cos (kx), (d) none of these ? ANS: (d) None of the above are correct. F = -dU/dx, hence U = ½ kx2 U(x) x Potential energy curve for simple harmonic oscillator ? Is this an appropriate potential to use to describe interatomic interactions under all conditions? ANS: No! Consider what happens to U as interatomic separation → . This doesn’t make sense…U should go to 0.

Solids, Liquids and Gases: Forces and Potentials U(r) r E0 r0 Morse curve – approximation to potential energy variation for two neutral atoms. Morse potential energy function 1.1 where r0 and E0 are as defined in the diagram to the left, and a is a constant. U(r) r Harmonic oscillator potential Bottom of interatomic potential curve (i.e. close to equilibrium) may be approximated by harmonic oscillator potential.

Solids, Liquids and Gases: Temperature and Changes of Phase You “intuitively” know that increasing the temperature (T) increases the average energy of the atoms. One of the aims of this course is to show you that the concept of temperature is rather more involved than this (…..entropy). However, for now, we’ll treat temperature as a good measure of the average energy of the atoms. U(r) r With increasing temperature the inter-atomic bond length increases (centre of oscillations shifts to larger r). Hence object expands at higher temperatures. (Explanation for thermal expansion somewhat more complex than this – we’ll return to this point later).

Solids, Liquids and Gases: Temperature and Changes of Phase As T is increased further, oscillation amplitude ↑ until atoms/molecules not bound to fixed centres (but still experience interatomic forces). Increasing the temperature still further causes the atomic kinetic energies to become so large that the atoms surmount the interatomic potential holding them together in the liquid. …but you know all this! ? If you add a small amount of hot water (at say 50°C) to ice water at 0°C will the temperature of the mixture initially: (a) rise to 25°C, (b) stay at 0°C, (c) rise to 50°C, (d) none of these. ? Years ago, my grandmother used to spray water over the vegetables in the cellar to protect them from frost. Is this simply an ‘old wives’ tale’ or can the presence of water help protect the vegetables?