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Unformatted text preview: Mat E 510 Thermodynamics of Solids Mat Mat E 510 Thermodynamics of Solids
Based on Prof. Roger Doherty’s course Roger Lecture #1 Yury Gogotsi
A.J. Drexel Nanotechnology Institute and Department of Materials Science & Engineering, Drexel University, Philadelphia, Pennsylvania, USA Introduction Introduction
Historically - study of heat engines Heat, q, and work, w, are examples of transfer of energy, U ε = work out / heat in = (Th – Tc) / Th. Concept of Entropy S - Direction of Change Defines Temperature, T (K) Equilibrium Chemical reactions / Structures Gibbs Free Energy, G How does thermo work?
4 basic postulates - the "Laws of Thermodynamics" • Zeroth Law: Establishes Temperature as an intrinsic property (like pressure). • First Law: Internal Energy is a State Function. • Second Law: Defines Entropy S that seeks a maximum value. dS = dq /T • Third Law: As T(K) -> 0, S -> 0 (usually if in Internal Equilibrium) Role Role of Thermo in Chemistry/ Materials
• These laws describe our world. They allow incredibly useful predictions starting from just simple thermal measurements: Specific heats, heats of reaction, vapor pressures, e.m.f. of electrochemical cells etc. - to predict all equilibrium structures, all chemical reactions, Phase diagrams, (usually easier to measure a PD and back calculate the thermodynamic properties) and the kinetics and thus resulting structures of structural transformations. So, an essential part of Materials Science and Engineering. Determines equilibrium. Compounds, Phases, Defects. Direction and kinetics of structural and chemical change. Hence Microstructure Phase diagrams Process design • • • • • P. Atkins, Four Laws that drive the Universe, Oxford Univ. Press, 2007 Materials Science and Engineering (MSE)
• • • • • The Relationship of Properties and Performance to "Microstructure". The Relationship of Microstructure to Composition and Processing. Modification of Processing to give New or Improved Properties. Thermo occurs in first and last activities but predominantly in the second activity. Distinction from Physical Chemistry or Solid State Physics ? Useful properties of Engineering Materials • MSE is still a largely empirical science but becoming, slowly, more predictive and steadily accelerating the pace of empirical development. Computational Computational Thermodynamics Phase Phase diagrams as projections of Gibbs energy plots Ternary system, projection from G-x1-x2 diagram Determination of most stable phase by Gibbs energy minimization
Phase with lowest Gibbs energy is the most stable. 1358.00 K 2846.16 K ‐71236.5 J Points on the solid lines for P = 1 atm are given for copper. ‐216494.2 J Effect of high pressure on the graphite to diamond transition
Where available, density (i.e. molar volume) data for solids and liquids are employed in REACTION (the “VdP” term) although their effect only becomes significant at high pressures. (However, unlike EQUILIB, compressibility and expansivity data are NOT employed.) At 1000 K and 30597 atm, graphite and diamond are at equilibrium (ΔG=0) Here, carbon density data are employed to calculate the high pressure required to convert graphite to diamond at 1000 K. The volume of diamond is smaller than graphite. Hence, at high pressures, the “VdP” term creates a favorable negative contribution to the enthalpy change associated with the graphite → diamond transition. Pidgeon Process for the Production of Magnesium
Equilibrium Mg partial pressure developed at the hot end of the retort
Water-cooled vacuum connection also condenses alkalis 1423 K MgO‐SiO2 phase diagram: Note: MgO(s) and SiO2(s) can not coexist. Chemical Chemical Equilibria Interaction Interaction Of ZrC with Chlorine Thermodynamic analysis for ZrC chlorination: equilibrium amount of species vs. T for 1 (a), 3 (b), 5 (c), and 10 moles (d) of Cl2. Software: FactSage (GTT Tech., Germany)
G. Yushin, Y. Gogotsi, and A. Nikitin, Carbide Derived Carbon, in Nanomaterials Handbook., Y. Gogotsi, Editor. 2006, CRC Press Definitions
• • • • • • • • • • System Surroundings Open system Closed system Isolated system Extensive property Intensive property Equilibrium Diathermic Adiabatic • • • • • • • • • • Thermodynamic temperature Classical thermodynamics Energy State function Heat Work Reversible process Heat capacity Latent heat Free energy Zeroth Zeroth Law of Thermodynamics
• If two bodies are each in Thermal Equilibrium with a third then they will be in thermal equilibrium with each other.
• They have the same "temperature" T - a property that determines thermal equilibrium. • Two bodies are in TE if, when placed in contact, their properties do not change (At constant pressure). • Under earth’s atmosphere (760mm of Hg) objects usually (760 are at that pressure. Zeroth Zeroth Law of Thermodynamics P. Atkins, Four Laws that drive the Universe, Oxford Univ. Press, 2007 Temperature Temperature
What is "temperature" ? How do we define it? • • • • Heat is defined in terms of temperature, so we cannot now define temperature in terms of heat. How would you explain or even describe "temperature"? Do the Joule experiment in a thermally insulated container. The liquid gets "hotter" What do we mean by that? Your finger will tell you it is different. The properties will change, so measure a property: • Density falls (volume expands) • A coil of wire in the water will have increased electrical resistance. • Salt solubility in water rises (higher ionic conductiv ity). (hi • So how can we measure this property, T ?? With a thermometer ! What is a thermometer? A device for measuring temperature – The zeroth law is the basis of the existence of a thermometer. Measuring Measuring the Temperature
Something that has a measurable property that changes when its condition of thermal equilibrium changes (energy added or taken away) : • Hg or alcohol in glass. Different thermal expansion (by volume) between glass and liquid. Bulb plus a fine capillary to enhance precision. Resistance thermometer. Long thin wire, high R(ohms). Thermocouple: A + B joined twice. Voltage develops when the "temperatures" of the two junctions are different. Celsius scale: 0°C ice plus water at P = 1 atm; 100°C water plus steam at P = 1 atm • • • • • But these thermometers will all give slightly different temperatures. “Temperature dependence” of properties is only approximately linear. What does that mean? Or rather: What is the "right" temperature scale? Constant Constant volume gas thermometer
• • • Gas pressure P as a function of temperature. ALL GASES WITH BP << 0°C GIVE ESSENTIALLY SAME PLOT (CHARLES LAW) P = K T FOR "IDEAL GASES" PV = RT R = 8.31 J Mole-1K-1. V - volume of 1 mole of gas. T Absolute temperature T as (K, °C + 273.1). Kelvin. 1 mole contains Avogadro's # of molecules 6.02 x 1023. (H2, N2, O2, He, Ne, Ar). Molecular wt. - 2 g H2, 28 g N2… 4 g of He • So (before the 2nd law), "temperature" was a very difficult property acceptable only because familiar. Measured by constant volume gas th thermometer, CVGT, or by other thermometers calibrated by a CVGT. CVGT th CVGT Temperature Temperature Scales P. Atkins, Four Laws that drive the Universe, Oxford Univ. Press, 2007 Some Some Important Temperatures
• • • • • • • • • • • • • Absolute zero (precisely by definition): 0 K or −273.15 °C Coldest measured temperature: 450 pK or –273.14999999955 °C Water’s triple point (precisely by definition): 273.16 K or 0.01 °C Water’s boiling point: 373.1339 K or 99.9839 °C Incandescent lamp: ~2500 K or ~2200 °C Melting point of tungsten: 3695 K or 3422 °C Melting point of carbon: 3773.15 K or 3500 °C Sun’s visible surface 5778 K or 5505 °C Lightning bolt’s channel 28,000 K or 28,000 °C Sun’s core 16 MK or 16M°C Thermonuclear weapon (peak temperature) 350 MK or 350M°C CERN’s proton vs. nucleus collisions 10 TK or 10 trillion °C Universe 5.391×10−44 s after the Big Bang 1.417×1032 K 1.417×1032 °C Classical Classical vs Statistical Thermodynamics
• Classical thermodynamics – non-atomistic. Emerged in 19th century century before everyone was convinced about the reality of atoms. Statistical thermodynamics – accounts for bulk properties (Ludwig Boltzmann, end of 19th century) of matter in terms of its end constituent atoms. It is called “statistical”, because very large numbers of atoms are considered, not single atoms. At a given temperature, a collection of atoms consists of some in their lowest energy state (E0, ground state), some in the next higher energy state (E1), and so on (atoms can exist with certain and quantized energies – quantum mechanics) • Boltzmann Boltzmann distribution
Boltzmann distribution is a distribution function or probability measure for the distribution of the states of a system. The Boltzmann distribution for the fractional number of particles Ni / N occupying a set of states i which each respectively possess energy Ei: where kB is the Boltzmann constant (1.38x10-23 J/K), T is temperature, gi is the degeneracy, or number of states having energy Ei, N is the total number of particles: and Z(T) is called the partition function, which can be seen to be equal to For a single system at a well-defined temperature, it gives the probability that the system is in the specified state. The Boltzmann distribution applies only to particles at a high enough temperature and low enough density that quantum effects can be ignored. Boltzmann distribution E0 P. Atkins, Four Laws that drive the Universe, Oxford Univ. Press, 2007 Thermodynamic Thermodynamic temperature
• The Boltzmann distribution is often expressed in terms of β = 1/kT where where β is referred to as thermodynamic beta. The term or , which gives the (unnormalised) relative probability of a state, is called the Boltzmann factor. Ω(E)/ Ω (E0)= Ω - Population of state of energy, E0 - the lowest energy state β = 1/kT= 1/τ, where τ is sometimes called the fundamental temperature of the system with units of energy . β is a more natural parameter for expressing temperature than T itself. Thus, k is just a conversion factor from to β to T • • • • • Maxwell-Boltzmann Distribution P. Atkins, Four Laws that drive the Universe, Oxford Univ. Press, 2007 • Temperature is a parameter that summarizes the relative populations of energy levels in a system at equilibrium. • It tells us the most probably distribution of population of molecules over the available states of a system in equilibrium. • When β is low, many states have significant When many populations • When β is high, only the states close to the When lowest state have significant populations. • Water freezes at 0ºC (273 K) or β=2.65x1020 J-1 . Water boils at 100ºC (373 K) or β=1.94x1020 J-1 100ºC Temperature from View Point of Statistical Thermodynamics ...
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This note was uploaded on 02/12/2010 for the course MAT E 510 taught by Professor Yury during the Summer '09 term at Drexel.
- Summer '09