ChemE 260 Thermodynamic Temperature Scales

1
ChemE 260 Thermodynamic Temperature Scales The
Carnot Efficiency

• Dr. William Baratuci
• Senior Lecturer
• Chemical Engineering Department
• University of Washington
• TCD 6 F GCB 5 10 11

May 2, 2005
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Thermodynamic Temperature Scales

• From Ch 5
• 2nd Carnot Principle
• Therefore
• Thermodynamic Temperature Scales
• Operate a HE between two thermal reservoirs
• Measure QC, QH and W
• Calculate ?
• Arbitrarily assign a value to either TC or TH
• If we know the functionwe can calculate the
  other, unknown T.
• This is a Thermodynamic Temperature Scale

Baratuci ChemE 260 May 2, 2005
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QC/QH Fxn(TH, TC)
Algebra tells us that
Baratuci ChemE 260 May 2, 2005
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The Kelvin Relationship

• All of the T1 terms in fA and fB must drop out
  when they are multiplied together.
• Only true if the fxn has the form
• Conclusion
• Lord Kelvin
• Result

Baratuci ChemE 260 May 2, 2005
5
The Ideal Gas Temperature Scale

• Apply the 1st Law to Steps 1-2 and 3-4 carried
  out in a closed system to determine QH and QC.

• Use the definition of boundary work and CV for
  ideal gases.

• Results

Baratuci ChemE 260 May 2, 2005
6
Adiabatic Steps in a Carnot Cycle

• Apply the 1st Law to Steps 2-3 and 4-1

• Use the definition of boundary work and CV for
  ideal gases.

• Results

• Conclusion

Baratuci ChemE 260 May 2, 2005
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Ideal Gas Kelvin Scales

• The isothermal steps

• The adiabatic steps

• Combining yields

• The Ideal Gas Kelvin Scales are identical !

Baratuci ChemE 260 May 2, 2005
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Carnot Efficiency and COP

• Power
• Cycles

Refrigeration Cycles
Heat Pump Cycles
Baratuci ChemE 260 May 2, 2005
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Performance vs. Reservoir T

• All cycles shown here are reversible.

Baratuci ChemE 260 May 2, 2005
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The Relative Value of Energy

• 100 J of heat at 1000 K produces more work than
  100 J of heat at 300 K
• Heat energy available at a higher T is more
  valuable or has a higher quality.
• You can always completely convert work into heat
  at ANY temperature using friction.
• We can conclude that work is a more valuable form
  of energy than heat !

Baratuci ChemE 260 May 2, 2005
11
Next Class

• Next class
• Chapter 7 Entropy
• Here the 2nd Law finally boils down to an
  equation that we can use to analyze thermodynamic
  cycles.
• The Clausius Inequality leads to the definition
  of a new propertyentropy, S.
• CIDR Learning Styles Survey

Baratuci ChemE 260 May 2, 2005