Basic Thermodynamics - Jun 2012

Mechanical Engineering (Semester 3)

TOTAL MARKS: 100
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any four from the remaining questions.
(3) Assume data wherever required.
(4) Figures to the right indicate full marks. 1 (a) Distinguish between following with an example for each:
(i) Intensive and extensive property
(ii) Point and path function
(iii) Quasistatic and actual process.(12 marks) 1 (b) The readings t_A and t_B Celsius thermometers A and B agree at the ice point (0°C) and steam point (100°C), but eleswhere they are related by the equation t_A=l+mt_B+nt_B², where l, m and n are constants. When both the thermometers are immersed in a wall strirred bath. A registes 51°C whereas B register 50°C. Determine the reading on B when A registers 25°C.(8 marks) 2 (a) Define thermodynamic heat and work.(4 marks) 2 (b) Derive an expresson for displacement work for polytropic process.(6 marks) 2 (c) A spherical balloon has an intial diameter of 25 cm and contains air at 1.2 bar. Because of heating the daimeter of the balloon increases to 30cm and during the heating process the pressure is found to be proportional to the diameter, calculate the work done during the process.(10 marks) 3 (a) State and derive an equation for steady state steady flow process(8 marks) 3 (b) Show that energy is a property of system(6 marks) 3 (c) Air flow steadily at the rate of 0.5 kg/s through an air compressor, entering at 7m/s velovity, 100 kpa pressure, and 0.95 m³/kg volume and leaving at 5m/s, 700 kpa, and 0.19m³/kg. The internal energy of the air leaving is 90 kJ/kg greater than that of the air entering. Cooling water in the compressor jackets absorbs heat from the air at the rate of 58 k.W. compute the rate of shaft work inpute to the air in kW.(6 marks) 4 (a) Give Kelvin-Plank and Clausius statement of seconds law of thermodynamics and show that they are equivalent.(10 marks) 4 (b) A reversible heat engine operates between two reservoirs at temperatures of 600°C and 40°C. The engine drives a reversible refrigerator which operates between reservoirs at temperature of 40°C and -20°C. The heat transfer to the engine is 2000 kJ and the network output of the combined engine refrigerator plant is 360 kJ.
Evaluate the heat transfer to the refrigerant and net heat transfer to the reservoir at 40°C.(10 marks) 5 (a) State and prove "Clausius inequality".(6 marks) 5 (b) Define entropy and prove that it is a property of a system.(6 marks) 5 (c) 2 kg of water at 80°C are mixed adiabatically with 3 kg of water at 30°C in a constant pressure process of 1 atmosphere. Determine the increase in entropy due to the mixing process. Assume for water c_p=4.187 kJ/kg.(8 marks) 6 (a) Sketch and explain separating and throttling calorimeter to find out the dryness fraction of pure substance.(8 marks) 6 (b) Draw the phase equilibrium diagram for water on P-T coordinates indicating triple and critical point.(4 marks) 6 (c) Steam initially at 1.5 Mpa, 300°C expands reversibly and adiabatically in a steam turbine to 40°C. Determine the ideal work output of the turbine per kg of steam.(8 marks) 7 (a) Show that for reversible adiabatic process PV^y= constant with usual notations.(5 marks) 7 (b) Explain the following :
(i) Maxwell's relations
(ii) Clausius-Clapeyron equation(8 marks) 7 (c) 2 g of air undergoes a polytropic process from 330k and 0.15m³ to 550K and 0.02m³.
Determine : (i) Work transfer; (ii) heat transfer; (iii) change in enthalpy; (iv) change in entropy.(7 marks) 8 (a) Write a brief note on compressibility factor and compressibility chart.(4 marks) 8 (b) State Gibb's Dalton law of partial pressures and hence derive an expression for the gas R of a mixure of gases.(6 marks) 8 (c) A mixture of ideal gases consists of 3kg of nitrogen and 5kg of carbon dioxide at a pressure of 300 kpa and a temperature of 20°C. Find:
(i) Mole fraction of each constituent
(ii) The equivalent molecular weight of the mixture
(iii) The equivalent gas constant of the mixture
(iv) The partial pressure and partial volume
(vi) THe volume and density of the mixture.(10 marks)