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Δ S of Ideal Gases

Δ S of Ideal Gases. Δ S of Ideal Gases. We have an equation of state, so we can integrate the Tds equations Still have the problem of the variation of C v and C p with temperature. Two main approaches: Constant C’s (approximate) Variable C’s (“exact”). Use these substitutions:. v. v.

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Δ S of Ideal Gases

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  1. ΔS of Ideal Gases

  2. ΔS of Ideal Gases • We have an equation of state, so we can integrate the Tds equations • Still have the problem of the variation of Cv and Cp with temperature. • Two main approaches: • Constant C’s (approximate) • Variable C’s (“exact”)

  3. Use these substitutions: v v

  4. Approximate method: use c at average temperature: Good if ΔT not too large.

  5. Constant C method Can also be on a /mole basis.

  6. Variable C’s • Take the temp dependent part out and put it in tables • sO • See table A-17 page 849 for air as an ideal gas.

  7. Variable C’s • Take the temp dependent part out and put it in tables • sO • See table A-17 page 849 • Integrate the rest from the ideal gas law.

  8. Variable C’s Can also be on a /mole basis as in tables A-18 …. Can get sO’s from EES for N2,CO2, etc using P=100 kPa.

  9. Example 6-9

  10. Small Temp interval so similar results.

  11. Isentropic Processes of Ideal Gases • Same two options • Constant or variable c’s

  12. Constant C’s and Isentropic Where k = Cp/Cv and is found at the ave. Temp. • Three variations:

  13. Variable C’s and Isentropic • With, exp(sO/R) = Pr and T/Pr = vr: Get Pr and vr vs temp. from ideal gas table (A-17)

  14. Example 6-10: Compression ratio for a car engine If you use the constant C (or constant k) method, need iteration.

  15. Example 6-11: Isentropic compression of an Ideal Gas, He In fact, He is a perfect gas so k = constant = 1.667

  16. Ideal gas summary Constant C’s (approximate) Variable C’s (“exact”) General General Isentropic Isentropic

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