PYQ Bank

Write a short note on Brownian motion.

The molecules of a gas are made up of four non coplanar atoms. Enumerate the translational, vibrational and rotational degrees of freedom of each molecule. Hence obtain the specific heat at constant volume C_V of the gas. Does the value so obtained agree with the observed value in general? If not why?

The two atoms is a molecule of a gas interact according to the potential \phi(r) = \frac{A}{r^6} + \frac{B}{r^{12}} r being the separation distance between the two atoms. Determine A and B if the potential energy \phi(r) = \phi(r_0) at the equilibrium separation r = r_0.

State the basic assumptions of Debye theory of specific heat of solids and write the expression for C_V derived from this theory. Show that this expression yields the famous T^3 law of specific heat at low temperature. Discuss the extent to which the theory agrees (or disagrees) with observation on specific heat through the variation of the Debye characteristic temperature \Theta_D with temperature, in general.

Write a short note on Clausius Calpeyron equation.

Prove that \int_A^B \delta Q / T evaluated along a reversible path joining the states A and B does not depend on the path chosen. Hence define the entropy function S. Calculate the entropy change in an ideal gas undergoing a state change from (V, P) to (2V, P/2) for three suitably chosen different paths and show that the result turns out to be the same all the cases.

Prove the latent heat equation \left(\frac{\delta L}{\delta T}\right)_{sv} - \frac{L}{T} = C_s - C_p where C_s and C_p are specific heats of saturated vapour aid the liquid in contact with it respectively. Given the following values referring to 1\text{ gm} of water at 100^\circ\text{C} L = 539\text{ Cal/gm} \left(\frac{\delta L}{\delta T}\right)_{sv} = -0.64\text{ Cal K}^{-1}\text{ gm}^{-1} C_p = 1.01\text{ Cal K}^{-1}\text{ g}^{-1} Calculate C_s. Explain why the specific heat takes a negative value.

Two coils are connected in series and their total self inductance is 4.40 mH. When one coil is reversed, the total self-inductance is 1.60 mH. All the flux due to the first coil links the second coil, but only 40% of the flux due to the second coil links the first coil. Find the self-inductance of each of the coils and their mutual inductance.

Define quality factor for an A.C. circular and discuss the meaning of electrical resonance in a series LCR circuit. Explain the term sharpness of resonance.

Determine the energy of attraction between an electric dipole and a plane conducting surface at zero potential.

A deuteron of kinetic energy 40 keV is describing a circular orbit of radius 0.6 m in a plane perpendicular to a magnetic induction \vec{B}. Calculate the kinetic energy of a proton that describes a circular trajectory of radius 0.8 m in the same plane with the same \vec{B}.

A series LCR circuit has L = 20\text{ mH}, C = 0.5\ \mu\text{F} and R = 10\,\Omega. The circuit is driven by an alternating emf with amplitude 200\text{ V}. Calculate (i) resonance frequency (ii) the current at resonance frequency (iii) Q value and (iv) half width of the resonance current.

Derive the wave equations for \vec{E} and \vec{B} and solve one of these for plane wave propagation in an unbounded, homogenous dielectric medium. Further show that in a plane wave (\vec{E}, \vec{B}, \vec{K}) form a mutually orthogonal right-handed system.

A travelling electromagnetic wave is described by the equation. E_x(z, t) = 0.5 \cos (20t - 2z) Determine: (i) Speed of the wave, v (ii) Wavelength. \lambda (iii) Time period, T (iv) Direction of propagation

What was the basis for light to be accepted as an electromagnetic wave ? The \vec{E} vector in a light wave polarised in the (x, y) plane is expressed as \vec{E}(x, y, z, t) = \vec{E}_0 \sin\left[\omega t - k(x + y)\right] Determine the propagation and the polarisation vectors.

Write down the expression for the energy distribution for the black body radiations at temperature T. Show that this expression goes into the Rayleigh-Jeans distribution at one end of the frequency spectrum and the Wiens distribution at the other end.

A potential difference with a frequency of 50 cycles per second is applied to a coil of resistance 1 k ohms and inductance 2H. Calculate the power factor of the circuits.

Write a short note on Ruby laser.

Explain the terms resolving power and magnifying power of an optical instrument. On what parameter do these physical quantities depend in case of a telescope? For a given re-solving power what is the optimum magnifying power in this case ?

Define dispersive and resolving powers of a plane transmission grating and obtain expressions for the two. Show that the first and second order spectra produced by such a grating will never overlap when the incident light contains wave-lengths in the range 4000\text{\AA} to 7000\text{\AA}.