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

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

expansion coefficient quantities determined from experiments 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

Basic concepts Temperature people have a subjective perception of temperature Temperature but 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 temperature of body B temperature of body A

=: thermal equilibrium 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 ( 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

Thermodynamic System: Certain portion of the universe with a boundary possibility to define what is part of the system and what is surrounding Moveable wall which Surrounding 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

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

Zeroth law and temperature measurement Thermometer: System* with thermometric property parameter which changes with temperature System 3 (length, pressure, resistance, …) System 2 System 1 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

? X: X: X: 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

Defining temperature scales 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. Defining temperature scales Ratio of temperatures = Ratio of thermometric parameters For all thermometers we set: 1

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

Assign arbitrary value to the triple point (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:  independent of the gas type and pressure for empirical gas temperature with 3=273.16 degrees absolute or thermodynamic temperature William Thomson Kelvin, 1st Baron (1824-1907)

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

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 Celsius 1701-1744 Fixed points again: - steam point (2120F) - ice point (320F) Difference 180 degrees instead of 100 degrees Gabriel Daniel Fahrenheit 1686-1736

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

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

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

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

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

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 Example: Volume extensive temperature intensive V3=2V0 V2=V0 V1=V0 + = T1=T0 T3=T0 T2=T0 I II III

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

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

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

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 pressure heat capacity: Constant volume heat capacity: 1 2 Q Q m fixed position V=const. P=const.

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

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

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

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