Heat and Thermodynamics — DU B.Sc. (Prog.) Physical Science courses pertaining to Electronics Previous Year Question Papers

2. Attempt four questions in all. (a) Derive an expression for work done by an ideal gas during an isothermal expansion process. (b) Using first law of thermodynamics, prove: ES = Cr ET CP = Y where Es & Er are adiabatic and isothermal elasticity respectively. (c) An investor claims to have developed an engine working between 500 K and 250 K with efficiency 54%. Is his claim valid? Justify. (d) The average kinetic energy of a gas molecule at certain temperature is 6.21 x 10-21 J. Find the temperature. (e) From Wien's displacement law calculate the temperature of sun, given that Am = 4753 A and Wien's constant b = 0.2898 x 102 m-K. (f) Define microstate and macrostate for a thermodynamical system. Q2. (a) Using first law of thermodynamics, prove Hence show that for 1 mole of an ideal gas (b) Derive the equation of state for an ideal gas undergoing an adiabatic process in terms of pressure and volume. (c) Draw the PV diagram for a Carnot's Engine and explain. Calculate the net work done by a Carnot engine in one complete cycle. Also derive an expression for its efficiency. (4,4,7) Q3. (a) Write the expressions for four thermodynamic potentials - Internal Energy (U), Helmholtz function (F), Enthalpy (H) and Gibb's function (G). Derive four Maxwell's thermodynamical relations using these thermodynamic potentials. (b) Given W = (U-G)/T where G is Gibb's function and U the internal energy. Show that W is constant for an ideal gas undergoing an adiabatic process. (c) 50 g of water at 0°C is mixed with an equal mass of water at 100°C. Calculate the resultant increase in entropy. Given: specific heat of water is 1 cal g'°C-1 Q4. (a) Derive an expression for mean free path for molecules in a gas using zeroth order approximation. (b) Using kinetic theory of gases, obtain an expression for viscosity n of a gas and discuss its variation with temperature and pressure. (c) What do you understand by a black body? Calculate the energy radiated by a black body at a temperature of 200 K. Given Stefan's constant = 5.67x 108 MT3K4 in SI units. Q5. (a) Derive Plank's law of black body radiation. (b) Compare the basic postulates of Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics. (c) Deduce relationship between Entropy and thermodynamic probability. (6,4,5) Values of Constants: Boltzmann's constant, k = 1.38 × 10-23 JK-1 Universal gas constant, R = 8.31 Jmol--K-1