The Entropy Departure Function (11:22) (uakron.edu) Deriving the general formula for the entropy departure function is analogous to the derivation for the internal energy formula. There are two points of interest however: (1) The entropy formula for an ideal gas depends on volume (or pressure) as well as temperature, necessitating a contribution of lnZ to correct from S^{ig}(T,V) to S^{ig}(T,P). (2) When all is said and done, combining S with U (derived in 08.02) gives A (=U-TS) and A gives G (=A+PV), implying that other departure functions can be obtained by simple arithmetic applied to U and S.

Comprehension Questions: The RK EOS can be written as: Z = 1/(1-bρ) - aρ/(RT^{1.5}). 1. Use Eqn. 8.19 to solve for (S-S^{ig})_{TV}/R of the RK EOS. 2. Use Eqn. 8.27 to solve for (A-A^{ig})_{TV}/RT of the RK EOS. 3. Use Eqns. 8.22 and 8.27 to solve for (S-S^{ig})_{TV}/R of the RK EOS.

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## The Entropy Departure Function

The Entropy Departure Function (11:22) (uakron.edu)

Deriving the general formula for the entropy departure function is analogous to the derivation for the internal energy formula. There are two points of interest however: (1) The entropy formula for an ideal gas depends on volume (or pressure) as well as temperature, necessitating a contribution of ln

Zto correct fromS(^{ig}T,V) toS(^{ig}T,P). (2) When all is said and done, combiningSwithU(derived in 08.02) givesA(=U-TS) andAgivesG(=A+PV), implying that other departure functions can be obtained by simple arithmetic applied toUandS.Comprehension Questions: The RK EOS can be written as:

Z= 1/(1-bρ) -aρ/(RT^{1.5}).1. Use Eqn. 8.19 to solve for (

S-S)^{ig}_{TV}/Rof the RK EOS.2. Use Eqn. 8.27 to solve for (

A-A)^{ig}_{TV}/RTof the RK EOS.3. Use Eqns. 8.22 and 8.27 to solve for (

S-S)^{ig}_{TV}/Rof the RK EOS.