UNIVERSITY OF ABUJA. FACULTY OF ENGINEERING MECHANICAL ENGINEERING DEPARTMENT MASTERS OF ENGINEERING FIRST SEMESTER EXAMINATION - 2018/2019 SESSION COURSE TITLE: ADVANCED THERMODYNAMICS CODE: MEE 811 LEVEL: 800 UNITS: 3.0 INSTRUCTIONS: Answer FIVE Questions ONLY lll questions carry equal marks TIME ALLOWED: 3 HOURS QUESTION ONE Maxwell relations a. The equation of state of a certain substance is given by the expression V = © —Frand P the specific heat is given by the relation C, = A + BT where A,B and C are constants, Derive expressions for changes in internal energy, enthalpy and entropy for An isothermal process (3 marks) An isobaric process (3 marks) i idity of (2) = —(8) ° b. Verity the validity of (: oe = @), for steam at 250°C and 300kPa (3 marks) ©. Using the Clapeyron equation, estimate the value of the enthalpy of vaporization of refrigerant 134a at 20°C and compare it withthe tabulated value in the thermodynamics table (5 marks) QUESTION TWO Exergy and second law efficiency a. A heat engine that receives heat from a furnace at 1200°C and rejects waste heat to a river at 20°C has a thermal efficiency of 40%. Determine the second law efficiency of this power plant (3 marks) b. A piston- cylinder device initially contains 2 litres of air at 100 kPa and 25 °C. Air is now compressed to a final state 600kPa and 150°C. The useful work input is 1.2 kJ. Assuming the surroundings are at 100kPa and 25°C, determine i, Exergy of air at the initial and final states (3 marks)ii, The minimum work that must be supplied to accomplish this compression process (@ marks) iii, Second law efficiency of this process, (2 marks) ¢. Steam enters an adiabatic turbine at 6MPa, 600°C and 80“ and leaves at SOKPa, 100°C and 140 m/s. Ifthe power ‘output of the turbine is SMW, determine i, The reversible power output (2 marks) ii, The second law efficiency of the turbine (2 marks) Assume the surroundings to be at 25°C QUESTION THREE Entropy balance and Entropy generation a. Discuss the concept of entropy generation in thermodynamic processes (3 marks) b. Steam expands in a turbine steadily at a rate of 40,000kg/h entering at 8MPa and 500°C and leaving at 40kPa as saturated vapor. If the power generated by the turbine is 8.2MW, determine the rate of entropy generation for this process. Assume the surrounding medium is at 25°C (5 marks) c. Ait (Cp = 1.005k//kg°C) isto be preheated by hot exhaust gases in a cross-flow heat exchanger before it enters the furnace. Air enters the heat exchanger at 95kPaand 20°C at a rate of 1.6m3/s. The combustion gases (Cp = 1.10kj/ keg®C) enter at 180°C at a rate of 2.2kg/s and leave at 95°C. Determine i, The rate of heat transfer to the air (2 marks) ‘The outlet temperature of the air (2 marks) ‘The rate of entropy generation (2 marks) QUESTION FOUR Asentropic process a. Describe the ideal process and isentropic efficiencies for the following i. Adiabatic turbine (2 marks) Adiabatic compressor (2 marks) Adiabatic nozzle (2 marks) b. Combustion gases enter an adiabatic gas turbine at 827°C and 850KPa with a low velocity and leave at 425kPa. Treating the combustion gases as air and assuming an isentropic efficiency of 82%, determine the work output of the turbine (4 marks)c. Air enters an adiabatic nozzle at 400kPa and 547°C with low velocity and exits at 240mv/s. ifthe isentropic efficiency of the nozzle is 90%, determine the exit temperature and pressure of the air (4 marks) QUESTION FIVE ‘Real gases ‘a. Discuss enthalpy and entropy departure (2 marks) b. Determine the enthalpy change and the entropy change of nitrogen per unit mole as it undergoes a change of state from 225K and 6MPa to 320K and 12MPa by assuming i. Ideal gas behaviour (5 marks) By accounting for the deviation using generalized charts (7 marks) QUESTION SIX Closed systems a. One kg of Air in a piston cylinder arrangement at 1 bar,27°C is compressed to 5 bar and 27°C by two different mechanically reversible processes namely: i. Cooling at constant pressure followed by heating at constant volume ii, Heating at constant volume followed by cooling at constant pressure Calculate the heat and work requirements as well as change in internal energy AU and change in enthalpy AH of the air for each path and discuss your results. Assume that Lo0sky kok © = constant for air, Cy oxrioKy T & ia (14 marks) QUESTION SEVEN Steam cycles a. With the aid of sketches, explain i, Back pressure turbine (2 marks) ii. Pass-out turbine (2 marks) b. The boiler of a back-pressure turbine steam cycle produces 8kg/s of steam at 40 bar and 500°C. This is expanded to 2 bar with an isentropic efficiency of 0.88 ‘The pump is supplied with feed water at 0.5 bar and 30°C and delivers it to the boiler at 31°C, 40 bar. Calculate the net power output of the cycle (10 marks)