UPSC Physics Optional PYQs (CSE & IFoS)PYQs

What is an adiabatic process? Give three engineering examples of adiabatic processes which are in common use.

Define the efficiency of a Carnot Engine. An engine is designed to have an efficiency of 25\% and to absorb heat at a temperature of 267^\circ\text{ C}. Find the maximum temperature at which it can exhaust heat.

How one can obtain the various types of information about the physical conditions on the stellar surface using thermal ionization equation to interpret the stellar spectra.

Write a short note on Adiabatic demagnetisation.

Write a short note on Debye's theory of specific heat.

Mention the assumptions made & by Einstein in explaining the variation of specific heat of solids with temperature. Show how these assumptions were used to derive the formula for the specific heat of solids. How and why Einstein's theory fails at very low temperatures.

The RMS speed of oxygen molecules at 0^\circ\text{ C} is 460\text{ ms}^{-1}. What would be the RMS speed of Argon molecules (Mol. wt. = 40 gm/mole) at 40^\circ\text{ C} and at what temperature this speed would be double than at N.T.P.?

At the N.T.P., the mass of one litre of Hydrogen is 0.09 gm. Calculate the (i) RMS (ii) Mean and (iii) Most Probable Speed at 27^\circ\text{ C}.

Explain how very low temperatures can be produced by adiabatic demagnetisation.

The specific heat of a substance is found to vary with temperature in the following way c(T) = aT + bT^2 where c(T) is the specific heat at the temperature T and 'a' and 'b' are constants. Compare the average specific heat of the substance in the temperature range 0-T to the specific heat at the mid-temperature T/2.

Explain the concept of internal energy of a system. Formulate mathematically the first law of thermodynamics. Calculate the work done in an isothermal compression of a gas.

Write a short note on Carnot cycle.

Write a short note on Thermodynamic potentials.

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?

Write a short note on Brownian motion.

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.