Statistical Physics (PH-524) M.Sc Physics 2nd Semester
NIT Jalandhar
Dr. Arvind Kumar
Physics Department
e.mail. : [email protected] [email protected]
Contents of Course:
Chapter I: Review of Thermodynamics
Chapter II: Classical Statistical Mechanics
Chapter III: Quantum Statistical Mechanics
Chapter IV: Ideal Bose and Fermi Systems
Books:
1. Statistical Mechanics by RK Pathria and Paul D Beale, Elsevier
2. An introductory course of statistical mechanics by P B Pal, Narosa
3. Thermodynamics & Statistical Mechanics by W Greiner
4. An introduction to Thermal Physics by Schroder, Pearson
5. Statistical Mechanics, Kerson Haung, John Wiley & Sons
6. Problems in statistical mechanics by D A R Dalvit...
7. Problems & Solutions in statistical mechanics by Yug Kuo Lim
Statistical Physics (PH-524)
Section I
Review of Thermodynamics
Lecture 1.1
• An introductory course of statistical mechanics by P B Pal, Narosa
• Thermodynamics & Statistical Mechanics by W Greiner
Many particle system examples:
• Atoms or molecules in a gas, solids, plasma
• Quantum gas of electrons in metals
• White dwarf (e- gas)
• Nuclear matter (many neutrons and protons), core of neutron stars
Thermodynamics : Study the thermal properties of system at macroscopic level
Does not bother about the behaviour of atoms/ molecules at microscopic level
The macro and microscopic pictures are linked by Statistical mechanics.
Statistical mechanics describe the bulk
Thermodynamics is based on experimental observations and is covered by four
Basic Terminology in Thermodynamics
Thermodynamics system:
Any macroscopic
body consisting of large
no of atoms/molecules which is under investigation.
Three types of thermodynamic systems
(depending upon restrictions on walls)
1. Isolated system: Neither energy nor matter
through boundary. Total E and N of system remain Fixed. V also remain fixed. (N,V,E) are used to define macrostate of system.
2. Closed system: Energy exchanged, but not matter.
system in thermal contact with heat bath.
If system is in equilibrium with surrounding mean values for energy (related to T) is considered.
3.Open system: Energy and matter both can be exchanged. System in contact with heat bath and particle reservoir.
If system is in equilibrium with surrounding mean values for energy (related to T) and mean
value for particle number (related to chemical potential) are considered.
If the properties of system are same in every part of it, we call it homogeneous.
If the properties change discontinuously at certain marginal surfaces, system is called heterogeneous.
Homogenous part of heterogeneous system are separated by phase boundaries.
Thermodynamics Parameters/Variables/ state quantities:
• Certain physical quantities used to define the
macroscopic state of system e.g., P, T, V, S, E etc.
• Microscopic quantities, e.g., position ,
momenta are not state quantities
• Few state quantities are sufficient to describe
Two types of state quantities
(i) Extensive variables: depends upon the amount of substance in the system.
Examples: V, S, N
Extensive state quantity of heterogeneous system is additively composed of extensive state quantity of single phases.
(ii) Intensive variables: Independent of the amount of substance in the system. Might assume different
Examples:
Every intensive variable has corresponding
Thermodynamics State: By defining the values of thermodynamics state variables we can define the State of thermodynamic system.
Examples:
Fluid system : (P,V,T)
Dielectric system: (E,P,T), Here P denotes polarization
Magnetic system: (M,B,T)
Thermodynamic Equilibrium:
• Equilibrium refers to the state of system which
do not change with time
• Closely related to the observation time
• A macroscopic phenomenon
• Macroscopic: Length and time scale much
•
On scale of molecular motions equilibrium
is not a instantaneous property but
associated with the long observation time
•
For large scale consideration observation
time cannot be too large otherwise
Thermal equilibrium : Related to temperature
Two systems in thermal equilibrium with each other Means they are at same temperature (intensive
Property).
Zeroth law : If two thermodynamic systems say A
• Concept of temperature can be extended to
systems which are not as a whole in thermal equilibrium.
This is possible only, when we can divide system into partial systems such that they can be assigned local temperature.
System is not in global equilibrium.
• To measure T, not necessary to put the measuring
Mechanical equilibrium: Uniformity of pressure
Chemical equilibrium: Constancy of chemical
composition
Thermodynamic equilibrium corresponds to situation when system satisfy all possible equilibrium
conditions and state of system does not change with time.
Equation of State (EoS)
The relation between thermodynamic parameters
of a system which is in thermodynamic Equilibrium.
Examples
Ideal gas
EoS for ideal gas (at high T and low P)
PV = NkT (n = no of moles)
nNA = N (N = total no of particles,
NA is the Avogadro no of particles)
PV = nNAkT=nRT
(ii) For real gases (vander Waal’s EoS)
Thermodynamic Transformations: Change of
thermodynamic system from one equilibrium state to other equilibrium state.
Irreversible process: These processes do not proceed in reverse direction.
e.g. Almost all processes of daily life, expansion of gas from small to larger vol., processes which
produce frictional heat.
Reversible Process: These processes proceed over equilibrium state.
Reversible processes are simulated by very small changes in the state variables such that equilibrium state is slightly disturbed.
This is allowed if changes happen sufficiently slowly compared to relaxation time of system. Such processes are called quasi reversible.
Relaxation time is the time required for system to
Reversible processes can be of different types:
Isothermal process: T constant
Isobaric process: P constant
Isochoric process: V constant
Iso-entropic or adiabatic process: No heat exchange, entropy constant
State functions: These are thermodynamic quantities which depend only upon the state of system and
Exact differential
Thermodynamic parameters are related through state functions or EoS
Consider
Consider the change in the state of system from x0 to x through path C
Work: Definition of work in thermodynamics Is borrowed from mechanics
F is the force acting on the system.
Conventions: Energy added to the system :+Ve
Energy subtracted from the system : -Ve
Consider a gas in thermodynamic equilibrium in gas cylinder. Suppose the force F = PA is applied on
piston and it is compressed through distance dl
For dielectric or magnetic system we can define
Work done in changing particle composition by amount dN
Work is an inexact differential.
Work done on system in irreversible process is more
than in reversible process. System produce
most work in reversible process. In irreversible process a part of work is always converted
Into heat
Heat (A form of energy):
Definition
In above C is heat capacity.
Heat and also total heat capacity are an extensive Quantities.
Specific heat capacity is an intensive quantity
c = C/m.
Heat capacity may depend upon the external conditions under which heat is transferred and We thus define:
Specific heat capacity at constant pressure and constant volume
Internal Energy (E or U):
In thermodynamics we are interested in internal Properties of system and hence in internal energy.
Internal energy is associated with the internal degrees of freedom. For example: the kinetic energy of
molecular motion and potential energy due to molecular interactions.
Note that in thermodynamics internal energy will
not be calculated by observing the internal degrees of freedom. It will be treated as thermodynamic
