Definition of Temperature

Transcription

1 Definition of Temperature Ron Reifenberger Birck Nanotechnology Center Purdue University January 9, Lecture 1

2 A Brief History Prior to 18 th 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 18 th Century (1750 s); transition from rural to urban society start of Industrial Revolution; How is heat converted to work in a steam engine? 19 th Century ( ) scientists were encouraged to study engines and their efficiency; is a perpetual motion machine possible? Two Laws of Thermodynamics emerge 2

3 Year Electricity and Magnetism 1st Law Thermodynamics 2nd Law Thermodynamics ~1760 TIMELINES Francis Hauksbee - first electrostatic generator Charles de Cisternay Dufay - electrified objects repel as well as attract Bernoulli uses idea of atomic motion to calculate pressure Bishop Von Kleist & Cunaeus of Leyden - Leyden jar (first capacitor) Ben Franklin - simple theory of electricity; two polarities of charge J. Black - discovers heat capacity, latent heat; inherently contradicts the calorique theory Chales Coulomb; force law for electrostatics J. Watt invents steam engine (condenser) Wm. Cleghorn formulated coherent calorique theory Boulton and Watt - commercial steam engines; first attempts to define w ork, power, horsepower, etc. Count Rumford established connection between mechanical work and heat Count Rumford (Benj. Thompson) questions caloric theory while boring out canons in Bavaria 1800 Alexandre Volta first electric battery 3

4 Hans Christian Oersted magnetic field from current Andre Marie Ampere first theory of the magnetic field Michael Faraday primitive electric motor Herapath links heat w ith atomic motion Carnot formulates 2 nd Law; supports calorique theory 1827 Georg Ohm Ohm s Law 1830 William Sturgeon first electromagnet 1831 Michael Faraday electromagnetic induction 1833 Joesph Henry self inductance 1834 Heinrich Lenz Lenz s Law 1837 Samuel Morse first telegraph 1842 James Prescott Joule heat produced by J.R. von Mayer (heat + work) is electric current conserved; initial formulation of 1st Law Joule s quantitative experiments Waterston first suggests that energy s of gas molecules is proportional to temperature Gustav Kirchoff Kirchoff s laws of electric circuits Helmholtz: conservation of energy, 1st Law of Thermodynamics 1850s J.P. Joule quantified heat & work in many ways mechanical, electrical, etc.; Calorique theory of heat finally overturned 4

5 James Clerk Maxwell unified theory of electricity and magnetism Treatise on Electricity and Magnetism by James Clerk Maxwell Henry Row land rotating static charge creates magnetic field Clausius introduces concept of mean free path Maxwell introduces idea of a distribution function Clausius introduces concept of thermodynamic entropy; Loschmidt estimates the size of an atom Boltzmann extends Maxwell s mathematical derivation of distribution function w ith considerable physical insight Boltzmann s transport equation proves that the MB distribution function is the ONLY one possible for a gas in thermal equilibrium 1876 Alexander Graham Bell telephone 1877 Boltzmann: S=k B ln(w) 1879 Thomas Edison electric lamp 1884 Stefan-Boltzmann T 4 law connects thermodynamics with E&M 1886 William Stanley electric transformer and transmission of ac voltages 1887 Heinrich Hertz generation and detection of electromagnetic waves Clausius, Maxwell, Boltzmann kinetic theory of a gas (late 1800s) 1887 Oliver Heaviside reworks Maxwell s theory FOUR Maxwell equations Nikola Tesla alternating current; longdistance electrical transmission Gibbs publishes Elementary Principles in Statistical Mechanics 5

6 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

7 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

8 Example I: Water Wheel vs. Steam Engine Steam in Work is produced Steam in Water in = Water out + Work Water is conserved. Heat in?=? Heat out + Work Is Heat conserved? 8

9 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 o C, 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

10 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

11 The Big Picture Four Laws of Thermodynamics 0 th Law: Definition of thermal equilibrium 1 st Law: U = Q - W quantity of energy; in a closed system energy can be exchanged but it can not be created or destroyed 2 nd Law: Definition of Entropy quality of energy: when transforming organized, useful energy, some of it always deteriorates into disorganized, non-useable energy 3 rd 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 ). 11

12 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=23.5 o C) 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

13 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 Thermoscopes 13

14 A simple constant-volume gas thermoscope calibrated masses, m calibration mark gas substance whose temperature you want to measure moveable piston, area A Pressure Force = = Piston Area mg 2 units : [N / m ] = Pascal(Pa) 5 1atm= Pa T=C 1 P + C 2 A 14

15 Implementation of a Constant Volume Gas Thermoscope Experiment showed this was a particularly reliable thermometer T m P atm ρ h P P P P atm atm atm mg A ha A hg g T=C 1 P + C 2 1 atm = 760 mm of Hg = 760 Torr Thermometers have scales printed on them; thermoscopes do not. one click 15

16 Defining Temperatures using a Constant Volume Gas Thermoscope P o and P 100 are pressures measured at fixed temperature points. Can add (or remove) Hg calibration mark P atm =Const. P t P Volume V What is t C (temperature of liquid bath)? P t -P o t C = x 100 (for Celsius scale) P 100 -P o 16 Which gas is best??

17 Which Gas is Best? (measuring the boiling point of sulfur) P t As P t 0, all gasses give the same answer. Thermometers 17

18 All Temperature Thermometers Rely on Fixed Points ( ) t C = 5/9 (t F -32) t F = 9/5 t C + 32 Fixed Points In the 1840 s there were ~18 different thermometer scales; each country had their own! 18 Negative Temperatures?

19 Negative Temperatures? This value does not depend on gas used V 1 V 2 V 3 Defines Absolute Zero as o C T= t C (Kelvin Scale) Note that temperature DIFFERENCES are the same 19

20 The range of temperatures is enormous! Standard Temperature = 273 K ~ 20 orders of magnitude! 20

21 0 th 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