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The Carnot cycle

The Carnot cycle. T. a. b. T 2. T 1. c. d. s. Entropy changes in reversible processes. Various cases:. Adiabatic process: đq r = 0, ds = 0, s = constant. A reversible adiabatic process is isentropic. THIS IS NOT TRUE FOR AN IRREVERSIBLE PROCESS!. Isothermal process:.

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The Carnot cycle

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  1. The Carnot cycle T a b T2 T1 c d s

  2. Entropy changes in reversible processes Various cases: • Adiabatic process:đqr = 0, ds = 0, s = constant. A reversible adiabatic process is isentropic. THIS IS NOT TRUE FOR AN IRREVERSIBLE PROCESS! • Isothermal process:

  3. Entropy changes in reversible processes Various cases: • Isothermal: ideal gas case (du = 0; đq = -đw; Pv = RT)

  4. Entropy changes in reversible processes Various cases: • Isochoric process: We assume u = u(v,T) in general, so that u = u(T) in an isochoric process. Therefore, as in the case for an ideal gas, du = cvdT. Thus, provided cv is independent of T over the integration (really only true for ideal gas, but often good approx.).

  5. What about reversible paths? P DS > 0 (1) • Isobaric (P = const) • Isothermal (PV = const) • Adiabatic (PVg = const) • Isochoric (V = const) (2) (3) (4) DS = 0 DS < 0 V • For a given reversible path, there is some associated physics.

  6. The combined 1st and 2nd Laws The 2nd law need not be restricted to reversible processes: • đQ is identifiable with TdS, as is đW with PdV, but only for reversible processes. • However, the last equation is valid quite generally, even for irreversible processes, albeit that the correspondence between đQ & TdS, and đW & PdV, is lost in this case.

  7. Entropy associated with irreversible processes Universe at temperature T2 Q T1 T2 > T1

  8. Entropy associated with irreversible processes Isobaric Cp1, T1i Cp2, T2i dQ

  9. Entropy associated with irreversible processes Isobaric Cp1, T1i Cp2, T2i dQ2 dQ1 Tf Infinite heat reservoir

  10. Entropy associated with irreversible processes Isobaric Cp1, T1i Cp2, T2i dQ2 dQ1 Tf Finite heat reservoir Qin = Qout, otherwise Tf would not remain constant

  11. Entropy of mixing Definition of partial pressure Pj of a constituent in a mixture: Here, P is the pressure of the mixture, and xj is the kilomole fraction of the jth constituent gas: final state f initial state i n1 T, P n2 T, P n = n1 + n2 T, P = P1 + P2

  12. Entropy of mixing final state f initial state i n1 T, P n2 T, P n = n1 + n2 T, P = P1 + P2 P is the pressure of the mixture; Pj is the partial pressure and xj the kilomole fraction of the jth constituent gas, where Then,

  13. Entropy of mixing

  14. Maxwell’s demon

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