ChemE 260 Entropy Balances On Open and Closed Systems

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ChemE 260 Entropy BalancesOn Open and Closed
Systems

• Dr. William Baratuci
• Senior Lecturer
• Chemical Engineering Department
• University of Washington
• TCD 8 A BCB 6 10 Supplement

May 10, 2005
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Entropy Balance Closed System

• 1st Law

• 2nd Law, Internally Reversible Processes

• Boundary Work, Internally Reversible Processes

(Usually assume Wtot Wb.)

• Gibbs 1st Equation

• Entropy Balance Equation
• Integral Form
• Differential Form
• Rate Form

Baratuci ChemE 260 May 10, 2005
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Entropy Balance Open System

• General

• Steady-state, SISO

• Entropy generation within the system

Baratuci ChemE 260 May 10, 2005
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The 1st Law and Entropy

• 1st Law, Steady-state, Internally Reversible,
  SISO

• From the definition of entropy

• Gibbs 2nd Equation

• Integrating for an open system

Baratuci ChemE 260 May 10, 2005
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Mechanical Energy Balance Equation

• Combine all the equations from the previous slide

• The MEBE

Bernoulli Equation

• If Wnot b 0

Bernoulli Equation (incompressible fluid)
Usually, Wnot b Wsh

• If ?Ekin ?Epot 0

Baratuci ChemE 260 May 10, 2005
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Shaft Work PV Diagrams

• Polytropic Processes

or

• ? ?1

• ? 1

Baratuci ChemE 260 May 10, 2005
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PV Diagram Polytropic
Baratuci ChemE 260 May 10, 2005
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Summary Wsh Polytropic Processes
Process Type Real Fluids Ideal Gases
0
? 1 Isothermal
? ? 1 Polytropic
? ? constant Isentropic
? ? Isochoric
Baratuci ChemE 260 May 10, 2005

• Wsh is actially all work other than flow work.

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Next Class

• Problem Session
• After that
• Isentropic Efficiency
• Define an efficiency for a process by comparing
  actual performance to the performance of an
  isentropic process
• Nozzles, compressors and turbines
• New diagram HS Diagram
• Multi-Stage Compressors
• Intercooler HEXs reduce work input requirement

Baratuci ChemE 260 May 10, 2005
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Example 1

• Air is compressed from 1 bar and 310 K to 8 bar.
  Calculate the specific work and heat transfer if
  the air follows a polytropic process path with d
  1.32. Assume air is an ideal gas in this
  process.

Baratuci ChemE 260 May 10, 2005
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Example 2

• A turbine lets down steam from 5 MPa and 500oC to
  saturated vapor at 100 kPa while producing 720
  kJ/kg of shaft work. The outer surface of the
  turbine is at an average temperature of 200oC.
  Determine the heat losses from the turbine and
  the entropy generation in the turbine in kJ/kg-K.

Baratuci ChemE 260 May 10, 2005