UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Write a short note on Clausius-Clapeyron equation.

What is the most probable distribution of speeds in a large number of molecules of a gas and indicate the steps for its derivation.

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

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.

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}.

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.

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

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.

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.

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.

Write a short note on Clausius Calpeyron equation.

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.

What is population inversion ? Mention the methods of achieving population inversion. Explain the concept of negative temperature.

Write a short note on Debye theory of specific heat of solids.