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Thermodynamics: (developed in 19th^ century)
phenomenological theory to describe equilibrium properties of macro- scopic systems based on few macroscopically measurable quantities
thermodynamic limit (boundaries unimportant)
state variables / state functions:
describe equilibrium state of TD system uniquely intensive: homogeneous of degree 0 , independent of system size extensive: homogeneous of degree 1 , proportional to system size
intensive state variables serve as equilibrium parameters
state variables / state functions:
intensive extensive
T temperature
p pressure
H magnetic field
E electric field
μ chemical potential
S entropy
V volume
M magnetization
P dielectric polarization
N particle number
conjugate state variable: combine together to an energy
T S, pV, HM, EP, μ N (^) unit [energy]
Equilibrium parameters:
intensive state variables can serve as equilibrium parameters
Temperature (existence: 0
th law of thermodynamics )
T
1
T
2 colder characterizes state of TD systems warmer „bridge“ heat flow Fick‘s law heat current temperature gradient T 1 < T 2
Equilibrium parameters:
intensive state variables can serve as equilibrium parameters
Temperature (existence: 0
th law of thermodynamics )
T
1
T
2 colder characterizes state of TD systems warmer „bridge“ heat flow
T T
„bridge“ equilibrium
T
1
< T < T
Fick‘s law^2 heat current temperature gradient no heat flow
Equations of state:
consider TD system described by state variables subspace of equilibrium states: equation of state (EOS)
Ideal gas:
Boltzmann constant thermodynamic EOS
Equations of state:
consider TD system described by state variables subspace of equilibrium states: equation of state (EOS)
Ideal gas:
Boltzmann constant thermodynamic EOS response functions isobar thermal expansion coefficient isothermal compressibility reaction of TD system to change of state variables
Laws of Thermodynamics 1
st
law
internal energy
ideal gas (single atomic):
(equipartition)
Specific heat:
constant V
caloric EOS
Laws of Thermodynamics 1
st
law
internal energy
ideal gas (single atomic):
Specific heat:
constant p (equipartition)
caloric EOS
nd
law of thermodynamics
two equivalent formulations R. Clausius: there is no cyclic process whose only effect is to transfer heat from a reservoir of lower temperature to one with higher temperature T 1
T 2
heat flow heat flow
T
1
< T
2 W. Thomson (Lord Kelvin): there is no cyclic process whose effect is to take heat from a reservoir and transform it completely into work; there is no perpetuum mobile of the 2 nd^ kind Q Q T 1
heat flow work Q W
Laws of Thermodynamics 2
nd
law
Carnot engine
T 2 T 1 ~ Q 1 Q 2 W=Q 1 - Q 2 reversible Carnot process definition of absolute temperature T irreversible process
entropy as new state variable
Clausius‘ theorem cyclic process reversible cyclic process irreversible
Laws of Thermodynamics 2
nd
law
application to gas:
dS exact differential S(U,V) caloric EOS thermodynamic EOS
Thermodynamic potentials natural state variables convenient simple relations and response functions: specific heat adiabatic compressibility dS= internal energy (gas) (^) U(S,V)
Thermodynamic potentials natural state variables convenient simple relations
other variables: (S,V) (T,V)
Helmholtz free energy (gas) (^) F(T,V) Legendre transformation response functions specific heat isothermal compressibility
Thermodynamic potentials natural state variables convenient simple relations
other variables: (S,V) (T,V)
Helmholtz free energy (gas) (^) F(T,V) Legendre transformation Maxwell relation
