Notes Introduction to continuous systems and fields Certain mechanical issues require a continuous system. For instance, consider the issue of an elastic solid that is vibrating. Here, the oscillation is caused by each point of the continuous ...
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 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 ...
Notes Condition for steady Precession of Heavy Symmetrical top with one point fixed Consider the motion of a heavy symmetrical top spinning about the axis of symmetry, viz z'axis. The top is subject to a gravitational torque and is locked at its lower ...
Notes Heavy symmetrical top with one point fixed We can select a particular set of body axes such that the off-diagonal elements vanish and the expression of inertia only contains the diagonal elements. These axes are known as ...
