State Ising model and obtain the partition function (In Z) for 1D in the absence of an external magnetic field up to second order perturbation. Explain the physical significance of each term in the Hamiltonian and discuss the role of the coupling constant J.
See Answer →Using the Mayer f-function, show that the second virial coefficient B2 for a gas with a hard-sphere potential, (r),
is given as , where σ is the 3 diameter of the sphere. Here,
(r) = ∞ for r < 6 and
(r) = 0 for r > σ.
Derive the expression for the second virial coefficient B2 in terms of the intermolecular potential (r) using the approximation βεo <<1. Use the Lennard-Jones potential to outline its calculation.
How many photons are present in 1cm3 of radiation at 727°C? What is their average energy?
Explain Pauli's paramagnetism. Show that at T = 0 Pauli's paramagnetic susceptibility is given by
where u" is the intrinsic magnetic moment of the particle of mass m.
See Answer →Obtain Fermi-Dirac distribution function. Draw it for T = OK and T > OK. What is its physical significance?
See Answer →Using the result show that the expression of density matrix (p) of a free particle in box of volume V in the canonical ensemble in the coordinate representation is given by L
Derive quantum Liouville equation. Write this equation for the Steady state.
See Answer →Consider a gas in lattice-gas model, in which gas contained in volume Vis assumed to be divided into fixed small cubic cells of volume Vo such that each of the (cell) can contain at most one atom. The system behaves as a set of distinguishable and independent cells in contact with a reservoir at temperature T and chemical potential µ. Obtain the expressions of canonical partition function and average number of particles .
Calculate relative fluctuations in the energy of the system about the mean value in canonical ensemble.
See Answer →Obtain an expression of probability of finding the system in the microstate k corresponding to energy Ek in canonical ensemble. Also, write the expression of canonical partition function.
See Answer →What is Gibb's paradox? Derive Sackur-Tetrode equation of entropy for a classical, ideal gas.
See Answer →Consider a single classical 1-D non-relativistic harmonic oscillator. Obtain x(t) and p(t) as a function of time t. Assume that initially at t = 0, the oscillator is at the maximum displacement xo and p(0) = 0. Plot its phase space trajectory for fixed total energy E.
See Answer →how that for any distribution where N is large, the distribution tends to a Gaussian or a normal distribution.
See Answer →Calculate the mean, and the variance of the following probability density functions:
i) Uniform , and
elsewhere.
ii) Rayleigh distribution
Explain Wallace's Rule of Nines. Explain the immediate steps of managing burns by fires and the first aid for skin burns.
See Answer →Discuss the occupational health hazards in repetitive tasks.
See Answer →Discuss the steps in recording and notification of occupational diseases.
See Answer →Define occupational hazards. Discuss physical hazards and its impact on health.
See Answer →Describe the elements and forms of participation. Explain in details the hierarchy of controls with examples.
See Answer →