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Control Volume Entropy Balance Illustrating an Impossible Process

ME 200 L28: Control Mass Entropy Balance and Directionality of Processes https://engineering.purdue.edu/ME200/ Spring 2014 MWF 0930-1020 AM Professor Wassgren Lecture by Robert Kapaku ; slides adapted from Prof. Gore TAs: Robert Kapaku rkapaku@purdue.edu Dong Han han193@purdue.edu.

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Control Volume Entropy Balance Illustrating an Impossible Process

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  1. ME 200 L28: Control Mass Entropy Balance andDirectionality of Processeshttps://engineering.purdue.edu/ME200/Spring 2014 MWF 0930-1020 AMProfessor WassgrenLecture by Robert Kapaku; slides adapted from Prof. GoreTAs: Robert Kapakurkapaku@purdue.eduDong Han han193@purdue.edu

  2. Control Volume Entropy Balance Illustrating an Impossible Process Given: Steam at 100oC, 1 bar is pressurized through a diffuser to 1.5 bars, 120oC and negligible velocity. Find: Find the change in entropy of steam in kJ/kg-K and comment on whether the diffuser can be adiabatic and the resulting impact. Assumptions: Change in PE neglected, No heat transfer, No work done other than flow work, Steady state, Steady flow, Mass is conserved. Equations: Starting with basic conservation equations from the equation sheet, we arrive at: Adiabatic diffuser with given pressure gain leads to decrease in entropy. In reality, this diffuser design will not function! The pressure gain will be less than what is assumed here. 2

  3. T-s Diagram and Diffuser Action (This diffuser will not work!) State 2: 1.5 bar, 120 C State 2: 1.5 bar, h2>h1, s2<S1 Saturated State: 1.5b bar, 111 C State 1: 1bar, 100 C State 1: 1bar, 100 C

  4. On the T-s diagram drawn to scale State 1 and State 2 are close to each other as illustrated below. State 2: 1.5 bar, 120 C State 1: 1bar, 100 C

  5. Entropy Balance Equation • Control Mass equations result from recognizing that there can be no inflows and outflows of mass • Analogous to and must apply simultaneously with the Conservation of Energy

  6. Control Mass Entropy Generation: Example 1 Given: Saturated liquid water at 10 bar is heated in a piston-cylinder device while maintaining pressure until the volume increases by a factor of 10. Assume the boundary temperature is equal to the water temperature. Find: (a) Work done in a reversible process, (b) Heat transfer in a reversible process, and (c) entropy production in kJ/kg-K, if the work done is (90% of theoretical value). Assumptions: Change in KE, PE neglected, Control mass. Equations: Important: Know why these equations are simplified this way! 6

  7. Control Mass Entropy Generation: Example 1 7

  8. Control Mass Entropy Generation: Example 1 179.9+273 8

  9. On the T-s diagram drawn to scale State 1 and State 2b 1 2

  10. On the p-v diagram drawn to scale State 1 and State 2 1 2

  11. In-Class Example ME 200

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