Using a Carnot cycle obtain the Clausius Clayperon equation. At normal pressure the ratio of densities of ice and water is 9 : 10. When 1 kilo-mole of ice is melted, the change in entropy is 22.2 \times 10^3\text{ JK}^{-1}. If the external pressure is increased by 10^5\text{ Nm}^{-2}, what will be the change in the melting point of ice?
A gas at a pressure P and temperature T has a density \rho. The velocity of sound in this gas is v. Obtain an expression for the degrees of freedom of the gas molecules. At STP, \rho = 1.3\text{ kg m}^{-3} and \text{v} = 330\text{ ms}^{-1}. Calculate the degrees of freedom.
Define Helmholtz free energy F and Gibbs free energy G. What does decrease in F and G signify ? Show that the internal energy U at temperature T is given by U = F - T \left( \frac{\partial F}{\partial T} \right)_V
Obtain an expression for the mean free path. Mention the correction introduced by Maxwell. Calculate the value of Avogadro's number if the mean free path of nitrogen molecules at STP is 6.85 \times 10^{-8}\text{ m}. The molecular diameter is 3.5\text{ \AA}.
Write a short note on Debye theory of specific heat of solids.
Obtain the characteristic impedance of the vacuum. Derive the expression used.
Derive the distribution law which explains the black body spectrum over the entire wavelength region. Using this relation determine the value of Wiens constant b.
An alternating voltage, v = V_0 \sin (\omega t + \phi) is applied to a series RL circuit through a switch. Find the sum total of the transient and steady currents. Find the conditions when transient current becomes
(i) zero, and
(ii) maximum
The self inductance of primary and secondary coils of a R.F. transformer is 10\text{ mH} each. When the coils are connected in series self resonating frequencies are 132.6\text{ kHz} and 108.3\text{ kHz}. Calculate the mutual inductance between the coils and the winding capacitance.
Using Gauss law find the electric field inside a cylindrical capacitor and hence derive the expression for its capacitance. Find the dielectric constant of the material inside a 50\text{ mm} long capacitor of capacitance 40\ \mu\text{F} having inner conductor of radius 1\text{ mm}, outer conductor of radius 10\text{ mm}. Which of the materials has such a value of the dielectric constant ?
Calculate the magnetic moment of a coil having 100 turns, each of area 10\text{ cm}^2 carrying a current of 1\text{ mA}, flowing for 1\text{ ms}. The coil is placed in a magnetic field of 0.5\text{ kg} which is perpendicular to the magnetic moment. Calculate the torque acting on the coil and the angular momentum transferred to it.
Write down Maxwell's equations in free space and hence show that the phase velocity of the electromagnetic wave is equal to the velocity of light in free space.
Give the concept of Fresnel's half period zones. Describe the salient features of Fresnel's diffraction pattern due to a straight edge, showing the intensity distribution. How are these features explained?
Write a short note on He-Ne laser.
A 3 MW laser beam which has a diameter of 1\text{ cm} is foccussed by a lens of focal length 5\text{ cm}. The wavelength of laser is 10,000\text{ \AA}. Calculate the intensity of the focal plane of the lens.
What is a quarter plate? A phase retardation plate of quartz has a thickness 0.1436\text{ mm}. Calculate the wavelength in visible region for which this plate will act as a quarter for plate. The refraction indices of quartz for ordinary and extraordinary rays are 1.5443 and 1.5533 respectively.
A plane transmission grating has 6000 lines per cm. Determine the angular separation between the two lines of sodium of wavelengths 5896\text{ \AA} and 5890\text{ \AA} in the second order spectrum. If the width of the grating is 2.5\text{ cm}, will these lines be resolved?
Why does a soap film appear coloured when is viewed by reflected white light? A thin film is illuminated by sodium light of wavelength 5900\text{\AA}. Its refractive index is 1.42. Calculate its minimum thickness so that it appears dark in reflected light.
What is spatial coherence ? Considering Young's two slit experiment, prove that the distance between the slits must be sufficiently less than (\lambda/\theta) for obtaining fringes of good contrast. \lambda is the wavelength of light used and \theta is the angle subtended by the source at the slits.
Write a short note on Phase and group velocities in dispersive media.
