Transcript Introductory remarks and basic concepts

Thermal Physics
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
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
Typical example of a thermodynamic relation :
2
C p  C V  VT
T
expansion coefficient
• quantities determined from
experiments
•no microscopic theory
compressibility
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
But:
relation of very general
validity independent of
microscopic details of the
system
kinetic theory,
Statistical mechanics
Basic concepts
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
temperature
of body A



temperature
of body B
Equality of temperature
body A of
temperature
body B of
temperature
A
sufficient long waiting
B
no further change in measurable properties of A and B
=: thermal equilibrium
 eA   eB
( 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
controls flux of
mechanical energy
Surrounding
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
System 3
property
parameter which
changes with
temperature
(length, pressure, resistance, …)
3 unchanged
1 and 3
come to equilibrium
System 1
2 and 3
in equilibrium
System 2
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
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
Constant–volume gas thermometer
X: change of the pressure with temperature
h determines the gas pressure
in the bulb according to p  gh
Const. volume
achieved by raising
or lowering R
Mercury level on left side of the tube const.
Defining temperature scales
1 For all thermometers we set:
2 X 2

1 X1
Ratio of temperatures =
Ratio of thermometric parameters
2 Assign a numerical value to a standard fixed point
triple point of water
Assign arbitrary value
3
to the triple point
  3
X
X3
(in general)
  3
P
P3
(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 P3  0
 P 
 



lim
empirical gas temperature g
3
P3 0 P3 
V
Note that P3 is not the pressure in
the triple point cell but the pressure
in the bulb of the thermometer which
can be made arbitraryly low.
with 3=273.16 degrees
 P 

absolute or thermodynamic temperature T  273 .16 K lim 
P3 0 P3 
V
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)
2
ice point (melting point of ice at pressure of 1 atmosphere)
Defined: steam  ice  100 degrees
with
steam  Psteam 

 

ice
 Pice  V
 1.3661
experiment
ice 
100
 273 .15
1.3661  1
Experiment shows:
100  ice  1.3661 ice
Note: Psteam/Pice is the pressure ratio measured
with the gas thermometer. Don’t confuse with
equilibrium vapor pressure of the water.
Triple point temperature 3 is 0.01 degree above ice  273 .15
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
 C  T  273 .15
Anders Celsius
1701-1744
Fixed points again: - steam point (2120F)
- ice point (320F)
Difference 180 degrees
instead of 100 degrees
180
9 C
C
 
  
100
5
F
Gabriel Daniel
Fahrenheit
1686-1736
F 
9 C
  32
5
State of a system
Remember:
Equilibrium (state) of a system
equilibrium state
Non-equilibrium
T=Tice= 273K
TL  TLe  Tice
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
Experiments show:
Boyle's Law
P V  const.
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
V  const. T
P V  const.
V  const. T
PV
 const.
T
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
PV  n R T
or
PV  N k B T
N=nNA # of particles
A general form treating P,V and T symmetrically
F(P, V, T)  0
for the ideal gas
F(P, V, T)  PV  nRT
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
1
extensive
Scale with the size of the system
variables
2
-independent of system size
-can be locally measured
intensive
Example: Volume extensive
but
temperature intensive
V3=2V0
V2=V0
V1=V0
+
T1=T0
I
=
T2=T0
T3=T0
II
III
Remark: In conventional thermodynamics one usually assumes extensive behavior
of the internal energy for instance.
+
=
U1=const. V0
U2=const. V0
I
II
U3=const. 2V0
III
Non-extensive
thermodynamics
But this is not always the case
Consider the energy E of a homogenously charged sphere:
EV
E
+
= E
Click figure for research
Article on nonextensivity
Compare
homework
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
Heat is not part of the systems
1/2
and not a state function
Do not confuse heat with the internal energy of a system
Sign Convention
Heat Q is measured with respect to the system
Q>0
Heat flow into the system
Q<0
Heat flow out of the system
Q>0
System
System
Heat Capacity and Specific Heat
Transfer of small quantity of
System @ T=T0
heat Q
System reaches new equilibrium at T=Tf>T0
System @ T=Tf
Temperature increase T=Tf-T0
1 Constant pressure heat capacity:
2 Constant volume heat capacity:
fixed position
m
Q
Q
V=const.
P=const.
Q
Q0 T P  const.
C P  lim
Q
C V  lim
Q0 T V  const.
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
n
M
specific heat , e.g.:
C
cV  V
n
CV
cM

V
M
specific heat: Material property independent of the sample size
CV(
) < CV(
)
however
specific heat:
cvM(
) = cVM(
)
But: specific heat
cvM
depends on material
1 kg
Q  M cM
V T
Specific heat at constant volume
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.
Q  M cM
P T
where
cP  const.
Q  n c P T
n cP  M cM
P