ChemE 260 Polytropic

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ChemE 260 Polytropic Isentropic Processes

• Dr. William Baratuci
• Senior Lecturer
• Chemical Engineering Department
• University of Washington
• TCD 7 ECB 6 3 - 5

May 9, 2005
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Relative Thermodynamic Properties

• Gibbs Equations for ideal gases

• Consider an isentropic process from a reference
  state (Tref, Pref, Vref) to any other state (T,
  P, V). Note, SoTref 0. Gibbs Eqns become

• Define Relative Properties(IG Properties
  Tables, functions of T only)

• Advantage of using Relative Properties

Baratuci ChemE 260 May 9, 2005
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Using Relative Properties

• Advantage of using Relative Properties

• Example

Air expands in aturbine from 1000 K and 1 MPa to
the surroundings at 100 kPa. If the air is an
ideal gas and the turbine is isentropic, what is
the temperature of the turbine exhaust ?
T (K) PR
540 8.3101
T2 8.6792
550 8.8893
By interpolation
Baratuci ChemE 260 May 9, 2005
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Isentropic Processes

• Assumptions Ideal Gas with constant and

• Key equations and

• Results

Baratuci ChemE 260 May 9, 2005
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Polytropic Processes

• Definition

• Other relationships

• An isentropic process is a polytropic process
  where

• Isobaric process

• Isothermal process

• Isochoric process

Baratuci ChemE 260 May 9, 2005
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PV Diagram for Polytropic Processes
Baratuci ChemE 260 May 9, 2005
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TS Diagram for Polytropic Processes
Baratuci ChemE 260 November 16, 2004
Baratuci ChemE 260 May 9, 2005
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Polytropic Process Paths on a TS Diagram

• Gibbs Eqns, IG, Constant Heat Capacities

• Isentropic process

• Isobaric process

• Isothermal process

• Isochoric process

Baratuci ChemE 260 May 9, 2005
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Boundary Work in Polytropic Processes

• Internally Reversible Processes

• ? 1 Isothermal

• ? ?1

• ? ? Isentropic

Baratuci ChemE 260 May 9, 2005
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Wb PV Diagram
Baratuci ChemE 260 November 16, 2004
Baratuci ChemE 260 May 9, 2005
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Next Class

• Entropy Balances
• Closed Systems No Mass Crosses the System
  Boundary
• Open Systems Mass Crosses the System Boundary
• Entropy Generation and ?Suniv
• The Mechanical Energy Balance Equation
• The Bernoulli Equation
• PV Diagrams Revisited
• Shaft Work on a PV Diagram !

Baratuci ChemE 260 May 9, 2005
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Example 1

• Saturated ammonia vapor enters an adiabatic
  compressor at -10oC and leaves at a pressure of
  1.0 MPa. Determine the work requirement per kg
  of ammonia for the compressor if the process is
  reversible.

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Example 2

• The pressure-volume diagram of a Carnot power
  cycle executed by an ideal gas with constant
  specific heat ratio g is shown in the diagram.
  Demonstrate that
• V4 V2 V1 V3
• T2 / T3 (P2/ P3)((g-1)/g))
• T2 / T3 (V3 / V2)g-1