ENGR 321 THERMODYNAMICS

Special Problems

Spring 2002

These problems together will count as one exam; individual problems are due on the dates indicated. Grades will be based on both the technical solution and the manner of presentation. Your answer should contain a clear description of your approach to the problem and the significance of your results. Simply having the correct numbers will not result in full credit. Each person submitting the work must sign the submitted paper. These problems are to be done as a group, not individually. It is unethical and a violation of the Engineering Honor Code to take credit for work you did not do, or to give credit to someone who did not participate in the solution. If you choose to solve some or all of these problems on a computer, your submission should include all of the work. "Computer" may mean a spreadsheet (Excel or Quattro), software like Mathcad or a Fortran, C, Pascal, etc. program.

1. (Due February 15) If you examine different books, you will find a wide variety of curve fits for the heat capacity of gases. The ideal gas heat capacity of oxygen, for example, is given by the following equations by different authors:

a. Sonntag, Borgnakke, Van Wylen:

with =T(K)/100 and c_p in kJ/kmol K

b. Felder and Rousseau:

with T in C and c_p in kJ/mol K

c. Reid, Prausnitz and Poling:

with T in K and c_p in J/mol K

d. Smith, Van Ness and Abbott:

with T in K

e. Sandler:

with T in K and c_p in J/mol K

f. Perry's Chemical Engineering Handbook (7^th Edition):

where T is in K and c_p in J/kmol K.

All of these equations supposedly represent the "exact" values presented in ideal gas tables. Compare the heat capacity values predicted by these equations in the temperature range of 300 to 3000K. Also, use each of them to find the enthalpy of oxygen in this temperature interval, and compare the predictions to the values in the ideal gas table. Comment on the results.

2. (Due March 25) An ammonia plant must compress 80 mol ammonia/second from a pressure of 5 atm to 50 atm. The initial temperature of the ammonia is 100C. Cooling water is available to reduce the temperature of the stream to 50C. Compressor and heat exchanger costs over the lifetime of the project may be approximate by:

C_comp = $258 P^1.003/yr

C_ex = $11.2 Q^0.928/yr

where P is the compressor power in kW and Q is the heat exchanger duty, also in kW. Electricity costs to power the compressor and cooling water costs for the heat exchanger are given by:

C_elec = $0.06/kW-hr

C_water = $0.16/GJ

The process is expected to operate 8000 hr/yr. The ammonia may be cooled to a temperature of no less than 50C. Design an economical system for this process. You may assume the ammonia acts as a ideal gas with a constant heat capacity of 3.5R. Your should consider at least the following possible configurations:

a. A single compressor with the given inlet temperature.

b. A heat exchanger followed by a single compressor.

c. Two compressors in series with a cooler in between. (Verify that the minimum total work is when the compression ratio (P_out/P_in) is the same for both compressors.)

3. (Due April 29) A process for producing fresh water from salt water is illustrated in the figure. The properties of the salt water may be assumed to be the same as those for pure water. The pump is adiabatic and reversible. The equipment costs of the pump and the heater can be neglected. However, electricity to run the pump costs $0.06/kW-hr. Heat for the heater is available at the following temperatures and costs:

T_heater(C) Cost ($/GJ)

160 3.17

184 3.66

254 5.09

Suggest a pressure P₂ and a temperature T₄ at which to operate the process. The temperature of stream 4 must be at least 10C less than the temperature of the heater. (If P₂ = 700 kPa and T₄ = 150C, m₇/m₁ = 0.0952.