UPSC Physics Optional PYQs (CSE & IFoS)PYQs

Calculate the temperature at which the average speed of \text{H}_2 molecules equals that of \text{O}_2 molecules at 350\text{ K}.

Write a short note on Equipartition of energy.

A and B are two huge blocks of same metal. The blocks are connected by a huge rod of the same material. The temperatures of A and B are 1500\text{ K} and 500\text{ K} respectively. The rate of heat conduction is 10^4\text{ J sec}^{-1}. Estimate the rate of entropy increase of the universe due to this process.

Define the thermodynamic energy functions. Using these functions establish the following relations:

(i) \left(\frac{\partial T}{\partial V}\right)_{\phi} = -\left(\frac{\partial P}{\partial V}\right)_V

(ii) \left(\frac{\partial P}{\partial T}\right)_V = \left(\frac{\partial \phi}{\partial V}\right)_T

(iii) \left(\frac{\partial T}{\partial P}\right)_{\phi} = \left(\frac{\partial V}{\partial \phi}\right)_P

(iv) \left(\frac{\partial \phi}{\partial P}\right)_T = -\left(\frac{\partial V}{\partial T}\right)_V

Write down Maxwell-Boltzmann distribution for the energy of molecules of a gas at temperature T. Find the energy at which this distribution peaks. Compute in eV the mean energy of molecules of a gas at 27^\circ\text{C},

Write a note on Thermal ionization.

Derive the expression for the specific heat of solid on the Einstein model. Comment on its short-comings.

Write a note on Production of low temperatures by adiabatic demagnetization.

Establish the relation C_p - C_v = T \left( \frac{\partial P}{\partial T} \right)_v \left( \frac{\partial V}{\partial T} \right)_p

One gram of hydrogen gas at 27^\circ\text{C} is compressed isothermally from 100 liters to 25 liters. Calculate the energy needed.

Write down the general expression for the Joule-Kelvin effect and define Joule-Kelvin coefficient, \mu. Show that for an ideal gas \mu = 0.

Establish that for an adiabatic process in an ideal gas T V^{\gamma-1} = \text{constant}. where the symbols have their usual meanings,

The density of steam at 100^\circ\text{C} is nearly 0.60 \times 10^{-3}\text{ kg/litre} and its latent heat is 2.31 \times 10^6\text{ J/kg}. Calculate the change in the boiling point of water if air pressure changes from 76.0\text{cm} to 70.0\text{cm} of Hg.

Write down the Maxwell-Boltzmann law for the distribution of speeds c of molecules in a gas. Show the distribution graphically for the temperatures T and 2T; also write down the expression for average value of c^3.

Calculate the work done in compressing adiabatically 10^{-3}\text{ kg} of air initially at STP to one-half its original volume. (Give density of air at \text{STP}=1.293\text{ kg/m}^3 and \gamma = 1.4.

Write a note on Dilution refrigeration.

Thermal energy of a solid is given by the relation E = \int_0^{ u_m} \frac{h\nu g(\nu)d\nu}{e^{h\nu/k_B T} - 1} where u_m = k_B \theta_D/h, \theta_D being the Debye temperature. Given g(\nu) = 6N h^2 \nu(k_B \theta_D)^2, deduce the expression for E for T \ll \theta_D and discuss the temperature variation of specific heat for T \ll \theta_D. \left( \int_0^\infty \frac{x^3 dx}{e^x - 1} = 2.404 \right)

Write a note on Enthalpy as a thermodynamic potential.

A system is composed of two-level atoms, the excited state 1, being 0.10\text{ eV} above the ground state 0. Find the fraction of all atoms which will be in state 1 if the system is in thermal equilibrium at temperature 300\text{ K}.

Calculate the mean free path of molecules of \text{H}_2 gas at 20^\circ\text{ C} at atmospheric pressure. Assume the molecular diameter to be 2.00 \times 10^{-10}\text{ m}.