Definition of Temperature Ron Reifenberger Birck Nanotechnology Center Purdue University January 9, 2013 1 Lecture 1 A Brief History • Prior to 18th Century, society supports advances in medicine (health) and astronomy (navigation; time keeping) • Other realms of science were viewed as a purely philosophic endeavor – not much in the way of experiments • mid 18th Century (1750’s); transition from rural to urban society – start of Industrial Revolution; “How is heat converted to work in a steam engine?” • 19th Century (1800-1850) scientists were encouraged to study engines and their efficiency; is a perpetual motion machine possible? • Two “Laws of Thermodynamics” emerge 2 TIMELINES Year Electricity and Magnetism 1st Law Thermodynamics 2nd Law Thermodynamics Francis Hauksbee - first electrostatic 1706 generator Charles de Cisternay Dufay - electrified 1733 objects repel as well as attract Bernoulli uses idea of “atomic” 1738 motion to calculate pressure Bishop Von Kleist & Cunaeus of Leyden - 1745 Leyden jar (first capacitor) Ben Franklin - simple theory of 1746 electricity; two polarities of charge J. Black - discovers heat capacity, latent ~1760 heat; inherently contradicts the calorique theory 1760-75 J. Watt – invents steam engine (condenser) Chales Coulomb; force law for 1785 electrostatics Wm. Cleghorn – formulated coherent 1779 calorique theory Count Rumford (Benj. Thompson) 1790 questions caloric theory while boring out canons in Bavaria Boulton and Watt - commercial steam 1794 engines; first attempts to define w ork, power, horsepower, etc. Count Rumford – established connection 1798 between mechanical work and heat 1800 Alexandre Volta – first electric battery 3 Hans Christian Oersted – magnetic field 1819 from current Andre Marie Ampere – first theory of the Herapath links heat w ith “atomic” 1820 magnetic field motion 1821 Michael Faraday – primitive electric motor Carnot formulates 2nd Law; supports 1824 calorique theory 1827 Georg Ohm – Ohm’s Law 1830 William Sturgeon – first electromagnet Michael Faraday – electromagnetic 1831 induction 1833 Joesph Henry – self inductance 1834 Heinrich Lenz – Lenz’s Law 1837 Samuel Morse – first telegraph James Prescott Joule – heat produced by J.R. von Mayer – (heat + work) is 1842 electric current conserved; initial formulation of 1st Law 1843-49 Joule’ s quantitative experiments Waterston first suggests that energy 1845 of gas “molecules” is proportional to temperature Gustav Kirchoff – Kirchoff’s laws of 1846 electric circuits Helmholtz: conservation of energy, 1st 1847 Law of Thermodynamics 1850s – J.P. Joule – quantified heat & work in many ways – mechanical, 1850s electrical, etc.; Calorique theory of heat finally overturned 4 Clausius introduces concept of mean 1858 free path Maxwell introduces idea of a 1859 distribution function Clausius introduces concept of 1865 James Clerk Maxwell – unified theory of thermodynamic entropy; Loschmidt electricity and magnetism estimates the size of an atom Boltzmann extends Maxwell’s mathematical derivation of 1868 distribution function w ith considerable physical insight Boltzmann’s transport equation proves that the MB distribution function is 1872 the ONLY one possible for a gas in thermal equilibrium Treatise on Electricity and Magnetism by James 1873 Clerk Maxwell Henry Row land – rotating static charge 1875 creates magnetic field 1876 Alexander Graham Bell – telephone 1877 Boltzmann: S=kBln(w) 1879 Thomas Edison – electric lamp Stefan-Boltzmann T4 law – connects 1884 thermodynamics w ith E&M William Stanley – electric transformer 1886 and transmission of ac voltages Heinrich Hertz – generation and Clausius, Maxwell, Boltzmann – kinetic 1887 detection of electromagnetic w aves theory of a gas (late 1800s) Oliver Heaviside – reworks Maxwell’s 1887 theory – FOUR Maxwell equations Nikola Tesla – alternating current; long- 1888 distance electrical transmission Gibbs publishes Elementary Principles 1902 in Statistical Mechanics 5 Why did it take ~100 years to sort all this out? A confusion between Temperature and Heat. We all have a qualitative feel for what “heat”, “hot”, “cold”, etc. means, but how do we turn these qualitative feelings into quantitative concepts? The answer to this question relies on an understanding how microscopic properties (atoms) translate into macroscopic measurable quantities. The Science of Thermodynamics Thermodynamics fundamentally was developed to understand the relationship between heat and work 6 While developing the Science of Thermodynamics, many Fundamental Conceptual problems arise I. Is Heat Conserved? II. Is Cold the Opposite of Hot? III. How to Quantify Temperature? ……. Without a Science of Thermodynamics, many of these basic concepts are not well-defined 7 Example I: Water Wheel vs. Steam Engine Steam in Steam in Work is produced Water in = Water out + Work Water is conserved. Heat in ?=? Heat out + Work Is Heat conserved? 8 Example II: Is “Hot” the opposite of “Cold”? • Most people would claim that “Hot” and “Cold” are opposites. • To make something hot, we add heat (measured in thermal units) because heat is energy. • You can always provide “more heat” by adding more energy, so you can always make an object “hotter”. • Therefore, by subtracting energy, you must have “less heat”; it follows that an object will get colder. • But….., experiment shows you can only cool to -273.15oC, you can't get any colder. • Since you can’t go any colder, you cannot continue to subtract more heat (or add “more cold”)? • How then can “cold” be the opposite of “hot”? • “Cold” is only a word used to describe the “absence of heat”. 9 Example III: Temperature – a way to quantify the “hotness” or “coldness” of an object Which object is colder? Styrofoam cup Piece of metal You can’t even trust your sense of touch! 10 Thermodynamic Laws The Big Picture Four Laws of Thermodynamics 0th Law: Definition of thermal equilibrium 1st Law: U = Q - W – quantity of energy; in a closed system energy can be exchanged but it can not be created or destroyed 2nd Law: Definition of Entropy – quality of energy: when transforming “organized, useful” energy, some of it always deteriorates into “disorganized, non-useable” energy 3rd Law: The entropy of a system at zero absolute temperature is a well-defined constant because a system at zero temperature exists in its lowest energy (ground) state. Its entropy is determined only by the degeneracy of the ground state. (Nernst 1906-1912). 11 To sort through these issues it is useful to list some of the attributes of temperature • It’s a property usually associated with a system • It’s a strange quantity – what are its origins? • Not derived from Newton’s Laws of Motion! • Distinguish between scientific (T=23.5oC) and colloquial (hot, cold, lukewarm, etc.) use • Tightly coupled to local properties of well defined systems; e.g. “What’s the temperature of the earth?” is not a meaningful question • Associated with equilibrium: constant T • How do you measure temperature? 12 Highly accurate measures of temperature are hard to find! • based on easily measured property of a common substance • easy to calibrate • the physical property chosen to measure temperature should monotonically increase in value as T increases • physical property must be measurable over a wide range of temperatures • readily reproduced in other laboratories 13 Thermoscopes A simple constant-volume gas thermoscope calibrated masses, m calibration mark moveable piston, area A Force mg Pressure == gas PistonArea A units :[N / m2 ] = Pascal(Pa) 5 substance whose 1atm=1.01×10 Pa temperature you want to measure T=C1 P + C2 14 Implementation of a Constant Volume Gas Thermoscope Patm Experiment showed this was a particularly reliable thermometer m ρ h mg P Patm A hA g Patm A P hg T atm T=C1 P + C2 1 atm = 760 mm of Hg = 760 Torr Thermometers have scales printed one click on them; thermoscopes do not. 15 Can add Patm =Const. Defining Temperatures (or remove) using a Constant Volume Hg Gas Thermoscope Pt Po and P100 are pressures calibration measured at fixed mark P temperature points. Volume V What is tC (temperature of liquid bath)? Pt -Po tC = x 100 (for Celsius scale) 16 P100 -Po Which gas is best?? Which Gas is Best? (measuring the boiling point of sulfur) Pt As Pt → 0, all gasses give the same answer. 17 Thermometers All Temperature Thermometers Rely on Fixed Points ( ) t = 9/5 t + 32 tC= 5/9 (tF-32) F C Fixed Points In the 1840’s there were ~18 different thermometer scales; 18 each country had their own! Negative Temperatures? Negative Temperatures? This value does not depend on gas used V1 V2 V3 Defines Absolute Zero as –273.15oC Note that temperature T= tC + 273.15 (Kelvin Scale) DIFFERENCES are the same19 The range of temperatures is enormous! “Standard Temperature” = 273 K ~ 20 orders of magnitude! 20 0th Law of Thermodynamics If objects A and B have the same temperature as object C, then objects A and B are also in thermal equilibrium with each other 21.