EML 6105 Advanced Thermodynamics and Statistical Mechanics

Test 1 Feb.20, 1995

1. Consider the compressor of a gas turbine engine in which air enters at ambient conditions, 100 kPa, 5oC, and leaves at 400 kPa. The compressor has an efficiency of 84%. Determine the work of compression, the reversible work for the actual change of state, and the irreversibility of the process per kg of air.

2. A solid aluminum sphere 0.1 m in diameter and initially at 200oC is allowed to cool to ambient temperature, 25oC. What is the irreversibility of this process? For aluminum, use a density of 2700 kg/m3 and specific heat of 0.9 kJ/kg K.

3. The saturation pressure of CO2 is 38.1 kPa at temperature of -90o C. The hig of CO2 from solid to vapor state is 574.5 kJ/kg and is approximately constant in this range of interest. Find the saturation pressure at 77.347oK. ( Ro = universal gas constant = 8.314 kJ/kmol K )

4. Derive expressions for ( T/ v)u and ( h/ s)v that do not contain the properties h, u, or s.

EML 6105 ADVANCED THERMODYNAMICS AND STATISTICAL MECHANICS 5/1/95

FINAL EXAMINATION

1. Steam enters a turbine at 4.0 MPa, 500oC, and 140 m/s and leaves as a saturated vapor at 100oC. The measured work output is 746.0 kJ/kg. The heat transfer from the outer surface of the turbine to the surroundings is 14.3 kJ/kg. Determine the availability change and the irreversibility for the steady-state steady-flow process within the turbine.

2. Prove that for a perfect gas internal energy and enthalpy are functions of temperature only.

3. Consider the steady-flow adiabatic combustion of gaseous ethylene(C2H4) with stoichiometric air, both at 25oC, and assume complete combustion and the products at 2570 K. Determine (a) the entropy change, (b) the availability change, and the irreversibility per kmol of fuel.

4. At 500 K the equilibrium constant for the reaction NO +0.5 O2 NO2 is 120. The initial reactants include 1 mole of NO, 10 mol of O2, and 40 mol of N2, and the pressure is maintained at 0.10 atm. Determine the moles of NO2 present at equilibrium.

5. Consider a system of three indistinguishable particles. The energies of each are restricted to values of 0, 1, 2, 3, and 4. If each of the energy levels has a degeneracy of unity and the total energy of the system is 6, determine (a) all possible distributions, and (b) the most probable distribution.

6. Consider a system of N indistinguishable monatomic molecules. The distribution of molecules in different energy levels follows Bose-Einstein model. The total internal energy U is constant. Assume that only translational motion of molecules is to be considered. Prove that the internal energy U = (3/2)NKT.