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

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

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

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

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

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

8. 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  1 System  2 System  3 (e.g. thermometer)

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

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

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

12. 2 Assign a numerical value to a standard fixed point triple point of water

13. Assign arbitrary value to the triple point (in general) (for the gas thermometer) :  depends on the gas pressure and the type of filling gas (O 2, Air, N 2, H 2 ) or more generally speaking  depends on the chosen thermometer However, experiments show:  independent of the gas type and pressure for empirical gas temperature with  3 =273.16 degrees absolute or thermodynamic temperature William Thomson KelvinWilliam Thomson Kelvin, 1st Baron (1824-1907) Note that P 3 is not the pressure in the triple point cell but the pressure in the bulb of the thermometer which can be made arbitraryly low.

14. Before 1954 gas temperature defined by two fixed points 1 Steam point (normal boiling point of pure water) 2 ice point (melting point of ice at pressure of 1 atmosphere) assigning a numerical value to the triple point temperature  3 Defined:degrees with experiment Experiment shows: Triple point temperature is 0.01 degree above  3 =273.16 degrees Note: P steam /P ice is the pressure ratio measured with the gas thermometer. Don’t confuse with equilibrium vapor pressure of the water.

15. Celsius and Fahrenheit scales Anders Celsius Anders Celsius 1701-1744 Temperature differences on the Kelvin and Celsius scale are numerically equal Ice temperature on Celsius scale 0.00 o C Gabriel Daniel Fahrenheit 1686-1736 Fixed points again: - steam point (212 0 F) - ice point (32 0 F) Difference 180 degrees instead of 100 degrees Click for Fahrenheit to Celsius converter

16. State of a system Remember:Equilibrium (state) of a system Non-equilibrium T=T ice = 273K T=T L >273K equilibrium state Steady state no time dependence

17. spanning the state space (here: 2 variables span a 2-dim.state space ) Example: temperature T and volume V can specify the state of a gas in accordance with the equation of state P=P(V,T) 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 independent variables Particular example of a PVT -systems -Equation of state of an ideal gas

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

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

20. 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) -for an ideal gas one obtains U=U(T) kinetic energy (disordered motion) + potential energy (particle interaction) internal energy U independent of the volume (because no particle-particle interaction)

21. Variables describing the state of a system can be classified into extensive intensive 1 2 variables Scale with the size of the system -independent of system size -can be locally measured Example: + = V 1 =V 0 Volume extensive but temperature intensive I II III V 2 =V 0 V 3 =2V 0 T 1 =T 0 T 2 =T 0 T 3 =T 0

22. Remark: In conventional thermodynamics one usually assumes extensive behavior of the internal energy for instance. + = I U 1 =const. V 0 II U 2 =const. V 0 III U 3 =const. 2V 0 Non-extensive thermodynamics Consider the energy E of a homogenously charged sphere: = + E E Compare homework But this is not always the case Click figure for research Article on nonextensivity

23. and not a state function Heat is not part of the systems Heat System  1 System  2 T1T1 > T2T2 Heat Q flows from  1 to  2 Heat is an energy transferred from one system to another because of temperature difference  1/2 Do not confuse heat with the internal energy of a system

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

25. Heat Capacity and Specific Heat System @ T=T 0 Transfer of small quantity of heat Q System @ T=T f System reaches new equilibrium at T=T f >T 0 Q m Q fixed position V=const. P=const. Constant pressure heat capacity: 1 2 Constant volume heat capacity: Temperature increase  T=T f -T 0

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

27. specific heat:Material property independent of the sample size C V ( ) < c V M ( ) = c v M ( ) however specific heat:

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

29. In general: Specific heat depends on the state of the system Classical limit 3R If thermal expansion of a system negligible and c V  const. c P  const. where Example: