UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Write a short note on Equipartition of energy.

Write a short note on Thermal ionization.

Assuming Clausius inequality, show that working between two given temperatures, all the engines of irreversible cycle are less efficient than a Carnot cycle and that all reversible cycles have the same efficiency as Carnot cycle.

Define entropy. Write a general expression for the elemental entropy change dS for 1 mole of an ideal gas. How would this become for cases where the change is (i) isothermal, (ii) isochoric, (iii) isobaric? Deduce expression for S_2 - S_1 for each of these cases, where (i) and (ii) refer to the initial and final stage entropies respectively. Constants C_p, C_v, R may be used, as needed, to express the results.

Derive an expression for the pressure exerted by an ideal gas on the walls of the walls of the chamber in terms of concentration of molecules (n), gas temperature (T) and a universal constant. Specifically discuss how T comes into the picture.

Derive an expression for the specific heat of solids in Einstein model. Explain Einstein temperature T_E. Find the value of specific heat when. (i) T \gg T_E (ii) T \ll T_E (iii) T = T_E/2

Under standard temperature and pressure a gas has density P = 1.29\text{mg/cc}, and the velocity (v) of sound propagation in it is 330\text{ m/s}. Calculate the number of degrees of freedom, the gas molecules may possess.

What Poynting vector ? Explain how the transport of electromagnetic energy is expressed quantitatively by Poynting vector.

A series circuit consisting of 410\text{ ohms} of resistance, 81.0\ \mu\text{H} of inductance and 225\ \mu\mu\text{F} of capacitance is excited by a constant voltage amplitude generator of variable frequency. At what frequency is the maximum power delivered?

An excess charge placed on an insulated conductor, resides entirely on its outer surface. Priestly checked his observation and showed that the inverse square law of force followed from it. Explain.

A harmonic emf is applied to a series circuit containing resistance, inductance and capacitance. Derive the expression for the current and condition for resonance.

Give the four basic experimental laws of electro magnetics in words and in mathematical form. Explain how they are modified to obtain the Maxwell's equations. Show how these equations lead to prediction about the speed at which e.m. waves are propagated in vacuum.

Define coherent length. A helium-neon laser emits radiation at wavelength \lambda = 632.8\text{ nm} with \Delta\lambda = 2\text{ pm}. Calculate the coherence wavelength.

A vibrating source is moving in a medium with speed V_s which is greater than the speed V of propagation of the wave in the medium. Apply Huygens principle to show that a conical wave front of half angle \sin^{-1}\left(\frac{V}{V_s}\right) is generated.

Give a mathematical explanation for the production of beats. Calculate the velocity of sound in a gas in which two wave of length 60.0\text{ cm} and 60.6\text{ cm} produce 5 beats per sec.

N coherent oscillation given by \zeta_K a \cos = (\omega t + K \phi) \quad K = 1, 2, 3, \ldots N are added, where a and \phi are independent of K. Deduce the expression for amplitude of the resultant oscillation.

Explain the general principle of laser action. What do you mean by population inversion ? Discuss the transitions involved in the ruby laser. A pulsed laser is rate at 10\text{mw}. It generates 3\text{ ns} wide pulses at frequency 500\text{ Hz}. Compute the instaneous power in the pulse.

The refractive indices of material of wavelength 5090\text{ \AA}, 5340\text{ \AA} and 5890\text{ \AA} are equal to 1.64, 1.640 and 1.630 respectively. Estimate the phase group velocities of light near \lambda = 5340\text{ \AA}.

An interference pattern is obtained by using two coherent sources of light, and the intensity variation is observed to be \pm 10\% of the average intensity. Determine the relative intensities of the interfering sources.

Give an account of the origin of optical activity in eqartz crystal. A wafer of crystalline eqartz of thickness. 2.945 \times 10^{-5}\text{ m} is used to change a beam of linearly polarised light (\lambda = 589\text{ nm}) into circularly polarised light. Find the difference in refractive index for the two waves in the crystal, assuming this to be minimum thickness that will produce the effect.