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 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 The principle of least action The notion of least action is a key concept in the Hamiltonian formulation. This is a more general kind of path variation where time and coordinates for position are both ...

Notes Euler's angles The orientation of a rigid body must be specified by three independent factors in order for the associated orthogonal transformation matrix to have the determinant +1 and to be used ...

Notes Force free motion of a symmetrical rigid body Let us choose the symmetry axis as the principle z axis, so that I1 = I2 and Euler's equations simplifies towhere A is some constant and we have chosen ...

Notes Type of the canonical transformation generated by W Consider a canonical transformation in which the new momenta pj are all constants of the motion α in particular is the constant of motion H, i.e., H(qj,pj)= α . Taking ...

Notes Angular momentum and Kinetic energy of motion about a point Angular momentum is a measure of the rotational motion of an object around an axis or a point. It is defined as the product of the moment of inertia (a ...