Assignment__9 - Assignment #9 PROBLEM 9.1 PROBLEM...

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Assignment #9 PROBLEM 9.1 PROBLEM STATEMENT: An engine operates on an ideal air-standard Stirling cycle. If the pressure and temperature at the beginning of the isothermal compression are 3.5 Mpa and 150 ° C, respectively, find the heat transferred to the regenerator during the isometric heat rejection process if the thermal efficiency of the engine is 40 percent. DIAGRAM DEFINING SYSTEM AND PROCESS: GIVEN: Air, Stirling Cycle 1 1 S P 3.5MPa,T 150 C 423K .40 η = = ° = = FIND: 41 q (kJ/kg) ASSUMPTIONS: 1. Air standard (IG, constant specific heats) 2. Internally Reversible 3. Isothermal Compression from state 1 to 2 4. Constant-volume heating from state 2 to 3 5. Isothermal Expansion from state 3 to 4 6. Constant-volume cooling from state 4 to 1 GOVERNING RELATIONS: 1. Carnot Thermal Efficiency: L H T 1 T = - 2. Entropy change for an ideal gas, isothermal: B B A p A T s s c ln T - = 0 B A P Rln P - PROPERTY DATA v c = 0.7296 kJ/ kg K g (Table 5s @ 150 °C) q OUT q IN P v 1 2 3 4 q REG Isothermal process at T 3 = T 4 Isothermal process at T 1 = T 2
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Assignment #9 QUANTITATIVE SOLUTION 1 1 OUT,12 2 1 1 2 IN,34 3 4 3 4 3 3 P T Rln q P T (s s ) 1 1 1 q T (s s ) P T Rln P η - - = - = - = - - - 4 1 3 2 P P P P = 1 3 3 3 T 423K 423K 1 0.4 1 T 705K T T 0.6 = - = - = = REG OUT,41 v 4 1 v 3 1 q q c (T T ) c (T T ) 0.7296kJ/kg K(705 423)K = = - - = - = g 205.7(kJ/kg) DISCUSSION OF RESULTS: For the ideal Stirling cycle, the thermal efficiency is the same as for a Carnot cycle, since all the external heat input and heat rejection is assumed to occur at constant temperature. This can only be achieved by using an ideal regenerator to transfer heat internally to raise the temperature of the compressed gas from T 2 to T 3 . In an actual Stirling cycle with non-ideal components, the efficiency will be substantially lower than Carnot efficiency, but still relatively high compared with other piston-cylinder cycles, such as Otto and Diesel.
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Assignment #9 PROBLEM 9.4 PROBLEM STATEMENT: An air-standard Otto cycle operates with inlet conditions of 1 atm and 27 ºC, and the compression ratio of the engine is 9:1. The maximum temperature reached in the cycle is 1800 K. The temperature dependent specific heat at constant volume for air can be approximated by ( 29 ( 29 - - = × - × g 3 6 2 v c 2.4 10 T 1.04 10 T kJ/kg K where T is the absolute temperature in the range 300 K T 1800K . Derive an expression for the efficiency of this Otto cycle. DIAGRAM DEFINING SYSTEM AND PROCESS:
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This note was uploaded on 04/20/2010 for the course M E 320 taught by Professor Deinert during the Spring '08 term at University of Texas at Austin.

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Assignment__9 - Assignment #9 PROBLEM 9.1 PROBLEM...

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