Module Specifications..
Current Academic Year 2023  2024
Please note that this information is subject to change.
 
Repeat examination Array 

Description The aims of the module are to analyse the behaviour of large number of quantum particles using statistical methods and to show how these can be used to calculate the structure and properties of solids, liquids, gases and light.  
Learning Outcomes 1. Explain the fundamental nature of the concepts of temperature and entropy at both the macroscopic and microscopic levels and their relationship. 2. Predict the microscopic states of systems of bosons and fermions and their total energy in the quantum and classical limits. 3. Outline the results of the particleinthebox model and notably the concept of density of states and its role in statiscal mechanics 4. Explain how the macroscopic properties of localised and classical particles can be obtained using the concept of partition function. 5. Outline the properties of the fermion gas in general and of the degenerate electron gas, in particular, to obtain a basic model for the structure of metals. 6. Outline the basic properties of the boson gas, in general, and of the photon gas in particular.  
All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml 

Indicative Content and Learning Activities
Lecture Series: Review of Classical Thermodymanics/Reformulation in terms of total differentials and partial derivatives Macroscopic state of thermodynamic systems, First and Second laws: Temperature and entropy, Intensive (U,V,N) and Extensive (T,P,mu) variables, Definition and importance of chemical potential mu, GibbsDuhem equation, Total differential of internal energy U, Thermodynamic potentials, Free energy F and thermostats. Lecture series: states of systems of quantum particles Microstates of individual particles, configurations of systems of particles. Distinguishable and indistinguishable particles, most probable configuration, fluctuations. Bosons, fermions and classical limit (MaxwellBoltzmann) Tutorials and Worked problems Counting, Arrangements and Combinations, Distributions (mean, variance, moments, Binomial, Poisson, Gaussian, Central Limit Theorem), classical vs quantum (indistinguishability) behaviour, Stirling approximation, Degeneracy/statistical weight of a quantum system (atom of hydrogen). Lecture Series: Methods of Statistical Physics Postulates, Extremum Principle, Lagrange multipliers, Work and heat, Statistical interpretation of entropy (Boltzmann postulate and Boltzmann constant), temperature and pressure Lecture Series: MaxwellBoltzmann Distribution The partition function, Definition, Partition function and thermodymanics, Domains of validity of M.B statistics for quantum systems, Applications of MaxwellBoltzmann distribution: The twolevel system, The ideal monoatomic gas, The onedimensional harmonic oscillator, Internal degrees of freedom, The diatomic molecule, The chemical potential of an ideal diatomic gas, Equilibrium conditions and dissociation Tutorials and Worked problems Maths: Gaussian integrals, gamma integrals and geometric series, Ideal gas law in terms of Boltzmann constant, number density of particles, partial pressures, Ideal gas and MB equilibrium, MB distribution of molecular velocities, Properties of ideal gas, Rigid rotator energy spectrum and partition function/temperature dependence, Gas of harmonic oscillators: spectrum, partition function, thermodynamic properties, Harmonic solid/Einstein temperature/DulongPetit law, Dissociation equilibrium of H2 molecule, Ionisation equilibrium of H atom/SahaBoltzmann equation, Spinflip system/paramagnets: order/disorder, partition function, entropy and magnetisation energy, adiabatic cooling and cryogenics Lecture Series: Quantum Statistics The Ideal Fermion Gas, General Properties, Applications:Free electron theory of metals, Model for the atomic nucleus, White dwarf stars. The Ideal Boson Gas, General Properties, Applications: The Photon Gas, The BoseEinstein Condensation Tutorials and Worked Problems Basic calculations of Fermi energy from electron density data, Total energy of the free electron gas, Blackbody radiator, Temperature dependence of Blackbody spectrum  
 
Indicative Reading List
 
Other Resources None  
Programme or List of Programmes  
Date of Last Revision  11NOV02  
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