Thermodynamics

Isentropic process:where P r is the relative pressure and v r is the relative specificvolume. The function s° depends on temperature only.The steady-flow work for a reversible process can beexpressed in terms of the fluid properties asFor incompressible substances (v constant) it simplifies toThe work done during a steady-flow process is proportionalto the specific volume. Therefore, v should be kept as smallas possible during a compression process to minimize thework input and as large as possible during an expansionprocess to maximize the work output.The reversible work inputs to a compressor compressing anideal gas from T 1 , P 1 to P 2 in an isentropic (Pv k constant),polytropic (Pv n constant), or isothermal (Pv constant)manner, are determined by integration for each case with thefollowing results:Isentropic:Polytropic:a P 2b P r2P 1 sconst. P r1a v 2b v r2v 1 sconst. v r12w rev v dP ¢ke ¢pew rev v 1P 2 P 1 2 ¢ke ¢pew comp,in kR 1T 2 T 1 2k 1w comp,in nR 1T 2 T 1 2n 1P 2Isothermal: w comp,in RT ln P 1P 2s° 2 s° 1 R ln P 11 kRT 1k12>k1k 1 caP 2b 1 dP 1 nRT 1n12>n1n 1 caP 2b 1 dP 1Chapter 7 | 401The work input to a compressor can be reduced by usingmultistage compression with intercooling. For maximum savingsfrom the work input, the pressure ratio across each stageof the compressor must be the same.Most steady-flow devices operate under adiabatic conditions,and the ideal process for these devices is the isentropicprocess. The parameter that describes how efficiently adevice approximates a corresponding isentropic device iscalled isentropic or adiabatic efficiency. It is expressed forturbines, compressors, and nozzles as follows:h T Actual turbine workIsentropic turbine work w a h 1 h 2aw s h 1 h 2sIsentropic compressor workh C Actual compressor workActual KE at nozzle exith N Isentropic KE at nozzle exit V 2a h 1 h 2a2h 1 h 2sIn the relations above, h 2a and h 2s are the enthalpy values atthe exit state for actual and isentropic processes, respectively.The entropy balance for any system undergoing anyprocess can be expressed in the general form asor, in the rate form, as w sw a h 2s h 1h 2a h 1S in S out S gen ¢S system123Net entropy transferby heat and mass123EntropygenerationS # in S # out S # gen dS system >dt123Rate of net entropytransfer byheat and mass123Rate of entropygenerationFor a general steady-flow process it simplifies toS # gen a m # es e a m # is i aQ # kT k2V 2s123Changein entropy123Rate of changein entropyREFERENCES AND SUGGESTED READINGS1. A. Bejan. Advanced Engineering Thermodynamics. 2nded. New York: Wiley Interscience, 1997.2. A. Bejan. Entropy Generation through Heat and FluidFlow. New York: Wiley Interscience, 1982.3. Y. A. Çengel and H. Kimmel. “Optimization of Expansionin Natural Gas Liquefaction Processes.” LNG Journal,U.K., May–June, 1998.4. Y. Çerci, Y. A. Çengel, and R. H. Turner, “Reducing theCost of Compressed Air in Industrial Facilities.”International Mechanical Engineering Congress andExposition, San Francisco, California, November 12–17,1995.5. W. F. E. Feller. Air Compressors: Their Installation,Operation, and Maintenance. New York: McGraw-Hill,1944.6. M. S. Moran and H. N. Shapiro. Fundamentals ofEngineering Thermodynamics. New York: John Wiley &Sons, 1988.7. D. W. Nutter, A. J. Britton, and W. M. Heffington.“Conserve Energy to Cut Operating Costs.” ChemicalEngineering, September 1993, pp. 127–137.8. J. Rifkin. Entropy. New York: The Viking Press, 1980.