ME 200 L28: Control Mass Entropy Balance and Directionality of Processes ME 200 L28: Control Mass Entropy Balance and Directionality of Processes Spring 2014 MWF AM Professor Wassgren Lecture by Robert Kapaku; slides adapted from Prof. Gore TAs: Robert Kapaku Dong Han

Control Volume Entropy Balance Illustrating an Impossible Process 2 Given: Steam at 100 o C, 1 bar is pressurized through a diffuser to 1.5 bars, 120 o C 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.

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

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

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

Control Mass Entropy Generation: Example 1 6 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: StP barT, Cv, m 3 /kgv f, m 3 /kgv g, m 3 /kgx (10 -3 ) (10 -2 )1.1273(10 -3 ) Important: Know why these equations are simplified this way!

Control Mass Entropy Generation: Example 1 7 StP barT, Cu, kJ/kgu f, kJ/kgu g, kJ/kgx StP barT, Ch, kJ/kgh f, kJ/kgh g, kJ/kgx

Control Mass Entropy Generation: Example 1 8 StP barT, Cs, kJ/kgKs f, kJ/kgKs g, kJ/kgKx

On the T-s diagram drawn to scale State 1 and State 2b 21

10 12 On the p-v diagram drawn to scale State 1 and State 2

September 17th, 2010ME In-Class Example