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, 5^{o}C, 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 200^{o}C is allowed to cool to ambient temperature, 25^{o}C. What is the irreversibility of this process? For aluminum, use a density of 2700 kg/m^{3 }and specific heat of 0.9 kJ/kg K.

3. The saturation pressure of CO_{2} is 38.1 kPa at temperature of -90^{o} C. The h_{ig} of CO_{2 }from solid to vapor state is 574.5 kJ/kg and is approximately constant in this range of interest. Find the saturation pressure at 77.347^{o}K. ( R_{o }= 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, 500^{o}C, and 140 m/s and leaves as a saturated vapor at 100^{o}C. 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(C_{2}H_{4}) with stoichiometric air, both at 25^{o}C, 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 O_{2 }NO_{2} is 120. The initial reactants include 1 mole of NO, 10 mol of O_{2}, and 40 mol of N_{2}, and the pressure is maintained at 0.10 atm. Determine the moles of NO_{2} 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.