Assignment__8 - Assignment #8 PROBLEM 8.1 PROBLEM...

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Assignment #8 PROBLEM 8.1 PROBLEM STATEMENT: A thermodynamic cycle using air as the working fluid in a closed system is outlined below. The specific heats of air can be assumed constant throughout the cycle with values taken at the initial conditions. The four processes that make up the cycle are: Process 1-2: Air at standard conditions (State 1: 1 atm, 298 K) is heated at constant volume to state 2, where Process 2-3: The air at State 2 is expanded isobarically to State 3, where Process 3-4: The air is expanded isentropically until it returns to pressure P 1 at State 4. Process 4-1: The air is compressed isobarically to return it to State 1. (a) Sketch the diagrams of this cycle. Pay special attention to the relative slopes of the process lines. (b) Find the numerical value of the power cycle efficiency of this heat engine. GIVEN: Air, P 1 = 1 atm, T 1 = 298 K Process 1-2: Constant volume to P 2 =10P 1 Process 2-3: Constant pressure (isobaric) to v 3 =3v 2 Process 3-4: Constant entropy (isentropic) to P 4 =P 1 Process 4-1: Constant pressure (isobaric) to v 1 FIND: ASSUMPTIONS: Ideal gas, constant specific heats. GOVERNING RELATIONS: 1. For constant specific heats, 2. For an ideal gas, R = c P – c V and k = c P / c V 3. Ideal gas equation, 4. P-T relation for isentropic process, constant specific heats: 5. Thermal efficiency, QUANTITATIVE SOLUTION: a). The P - v diagram can be derived from the known processes. For the T - s diagram, note that for the constant volume process, and for the isobaric process,
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steeper than the isobaric processes. The diagrams for this cycle are shown below. T-s diagram P 2 3 1 3v 1 P 1 10P 1 v 1 4 v 4 dv = 0 dP = 0 ds = 0 P-v diagram T 3 dP = 0 ds = 0 dv = 0 2 4 dP = 0 1 s v b). The temperature of each state can be found in terms of T 1 . Also, the
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Assignment__8 - Assignment #8 PROBLEM 8.1 PROBLEM...

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