Introduction to Thermal Physics: Thermodynamics & Kinetic Theory

1. Thermodynamics • kinetic theory • statistical mechanics Thermal Physics Introductory remarks Thermal Physics ? What is the scope of thermodynamics macroscopic or large scale behavior of systems involving concepts like: - heat Typical problems - temperature - entropy heat work

2. What does it mean ? Of remarkable universality macroscopic or large scale systems electromagnetic radiation liquid solid magnet gas Thermodynamics: Theory based on a small number of principles generalizations of experimental experience

3. Typical example of a thermodynamic relation : expansion coefficient • quantities determined from • experiments • no microscopic theory compressibility But: relation of very general validity independent of microscopic details of the system Heat capacity at constant pressure/volume (Definition of CP/V and meaning of the relation later in this course) • Calculation of the actual magnitude of • - heat capacity • expansion coefficient • compressibility kinetic theory, Statistical mechanics

4. Basic concepts but temperature of body B temperature of body A people have a subjective perception of temperature Temperature physical theory requires a precise definition of temperature Macroscopic bodies possess a temperature characterized by a number -Temperature is a scalar quantity -we can find out whether

5. body A of temperature body B of temperature Equality of temperature sufficient long waiting no further change in measurable properties of A and B =: thermal equilibrium ( is the empirical temperature in contrast with the absolute thermodynamic temperature T) Instead talking about bodies A and B let us introduce the concept of a system

6. Surrounding Thermodynamic System: boundary Certain portion of the universe with a possibility to define what is part of the system and what is surrounding Moveable wall which controls flux of mechanical energy real boundary (imaginary boundaries can also be defined) Here: gas enclosed by the boundary no particle exchange with surrounding Example of a closed system open: particle exchange possible

7. Zeroth law of thermodynamics: When any two systems are each separately in thermal equilibrium with a third, they are also in thermal equilibrium with each other. foundation of temperature measurement System 3 (e.g. thermometer) System 1 System 2

8. System 2 System 1 Zeroth law and temperature measurement Thermometer: System* with thermometric property parameter which changes with temperature System 3 (length, pressure, resistance, …) 3 unchanged 1 and 3 come to equilibrium 2 and 3 in equilibrium 1 and 2 in equilibrium temperature of 1= temperature of 2 Note: Thermometer requires no calibration to verify equality of temperatures * “small” enough not to influence 1/2

9. ? How to assign a numerical value to the temperature Common thermometers and corresponding thermometric property X Liquid-in-glass thermometers X: change of the level of the liquid with temperature resistance thermometer X: change of the resistance with temperature thermocouple X: change of the voltage with temperature

10. Defining temperature scales Ratio of temperatures = Ratio of thermometric parameters Constant–volume gas thermometer X: change of the pressure with temperature h determines the gas pressure in the bulb according to Const. volume achieved by raising or lowering R Mercury level on left side of the tube const. For all thermometers we set: 1

11. Assign a numerical value to a standard fixed point 2 triple point of water

12.  independent of the gas type and pressure for William Thomson Kelvin, 1st Baron (1824-1907) to the triple point Assign arbitrary value (in general) (for the gas thermometer) :  depends on the gas pressure and the type of filling gas (O2, Air, N2, H2) or more generally speaking  depends on the chosen thermometer However, experiments show: empirical gas temperature with 3=273.16 degrees absolute or thermodynamic temperature

13. degrees experiment is 0.01 degree above Triple point temperature 3=273.16 degrees assigning a numerical value to the triple point temperature 3 Before 1954 gas temperature defined by two fixed points Steam point (normal boiling point of pure water) 1 ice point (melting point of ice at pressure of 1 atmosphere) 2 Defined: with Experiment shows:

14. Celsius and Fahrenheit scales Click for Fahrenheit to Celsius converter Temperature differences on the Kelvin and Celsius scale are numerically equal Ice temperature on Celsius scale 0.00oC Anders Celsius1701-1744 - steam point (2120F) Fixed points again: - ice point (320F) Difference 180 degrees instead of 100 degrees Gabriel Daniel Fahrenheit 1686-1736

15. State of a system Remember: Equilibrium (state) of a system equilibrium state Non-equilibrium T=Tice= 273K T=TL>273K Steady state no time dependence

16. State of a system is determined by a set of state variables Properties which specify the state completely In the equilibrium state the # of variables is kept to a minimum Example: temperature T and volume V can specify the state of a gas in accordance with the equation of state P=P(V,T) independent variables spanning the state space (here: 2 variables span a 2-dim.state space) Particular example of a PVT -systems -Equation of state of an ideal gas

17. Experiments show: In the limit P->0 all gases obey the equation of state of an ideal gas Charles and Gay-Lussac's Law Boyle's Law animations from: http://www.grc.nasa.gov/WWW/K-12/airplane/aglussac.html

18. Ideal gas equation of state universal gas constant R=8.314 J/(mol K) R=NA kB can also expressed as where NA=6.022 1023 /mol: Avogadro’s # Experiment: const.=n R and kB=1.380658 10-23 J/K Boltzman constant # of moles or N=nNA # of particles

19. internal energy U A general form treating P,V and T symmetrically for the ideal gas State of a closed system in thermal equilibrium is also characterized by the internal energy U=U(T,V) kinetic energy (disordered motion) + potential energy (particle interaction) -for an ideal gas one obtains U=U(T) independent of the volume (because no particle-particle interaction)

20. Variables describing the state of a system can be classified into extensive Scale with the size of the system 1 variables -independent of system size -can be locally measured intensive 2 but Volume extensive temperature intensive Example: V3=2V0 V2=V0 V1=V0 + = T1=T0 T3=T0 T2=T0 I II III

21. U2=const. V0 U3=const. 2V0 U1=const. V0 I II III Non-extensive thermodynamics E E + Remark: In conventional thermodynamics one usually assumes extensive behavior of the internal energy for instance. + = But this is not always the case Click figure for research Article on nonextensivity Consider the energy E of a homogenously charged sphere: Compare homework =

22. Heat T1 > T2 System 2 System 1 Heat Q flows from 1to2 Heat is an energy transferred from one system to another because of temperature difference and not a state function 1/2 Heat is not part of the systems Do not confuse heat with the internal energy of a system

23. Sign Convention Heat Q is measured with respect to the system Heat flow into the system System Q>0 Q>0 System Heat flow out of the system Q<0

24. Q m Q Heat Capacity and Specific Heat System @ T=T0 Transfer of small quantity of heat Q System @ T=Tf System reaches new equilibrium at T=Tf>T0 Temperature increase T=Tf-T0 Constant volume heat capacity: Constant pressure heat capacity: 2 1 fixed position V=const. P=const.

25. n M Heat capacities are extensive: System 1 CV(1) CV (1+ 2)= CV (1) +CV(2 ) System 2 CV(2) , e.g.: Extensive heat capacity specific heat # of moles or the mass

26. CV( ) CV( ) specific heat: Material property independent of the sample size < however cVM( ) cvM( ) = specific heat:

27. cvM specific heat depends on material But: 1 kg Temperature increase Amount of heat Specific heat at constant volume

28. Specific heat depends on the state of the system In general: Example: 3R Classical limit If thermal expansion of a system negligible and cV  const. cP const. where