Notes Entropy of a classical ideal gas using the concept of microcanonical ensemble The microcanonical ensemble describes a system that is isolated and has a fixed total energy. For an ideal gas, the total energy of the system is the sum of the ...
Notes Gibb's paradox and its resolution Gibbs' paradox is a problem in statistical mechanics that arises when attempting to calculate the entropy of a mixture of two ideal gases. The paradox is that the entropy of ...
Notes Langevin's theory of Paramagnetism Consider a system of N atoms each of which has magnetic moment of magnitude μ. The Hamiltonian in presence of external magnetic field (B) isH (p,q) - μB Σ ...
Notes Theorem of equipartition of energy (Boltzman equipartition) From generalized equipartition theorem< xi, ∂H/∂xj > = ðij KBT...................1Many physical system have Hamiltonian which in classical transformation can be expressed aswhere Ai and Bi are …
Notes Polarisability per molecule in terms of Langevin's function In polar substance, the permanent dipoles are random oriented due to the thermal agitation. So the net dipole moment is zero. When an external field is applied, the dipoles align ...
Notes Thermodynamics behaviour of an ideal gas of photons (black body radiation) Consider an electromagnetic radiator enclosed in a fixed volume 'V' at a fixed temperature T. One can obtain such a system by making a cavity in any material and then ...
Notes Grand Cannonical Ensemble Each system in the microcannonical ensemble has the same fixed energy and the same amount of particles (N, V, E). This ensemble's system is a closed, isolated thermodynamic system (because ...
Notes Cannonical Ensemble The microcannonical ensemble is a general statistical tool but it is often very difficult to use practice because of difficulty in evaluating the volume of phase space. Hence cannonical ensemble ...
