1. ConcepTests in Chemical Engineering Thermodynamics Unit 2: Generalized Analysis of Fluid Properties Note: Slides marked with JLF were adapted from the ConcepTests of John L. Falconer, U. Colorado. Cf. Chem. Eng. Ed. 2004,2007

2. (a) (  P/  V)S (b) (  T/  V)U (c) (  U/  T)V (d) (  P/  T)V Day 22 MRs 22.1. Transform the expressions below in terms of Cp, Cv, T, P, and V. Your answer may include absolute values of S if it not associated with a derivative. (  S/  V) T

3. (a) Cv(  T/  P) V /T (b) (  T/  V) U (c) (  U/  T) V (d) (  P/  T) V Day 22 MRs 22.2. Transform the expressions below in terms of Cp, Cv, T, P, and V. Your answer may include absolute values of S if it not associated with a derivative. (  S/  P) V

4. (a) Cv(  T/  P) V /T (b) T(  V/  T) P /Cp (c) (  T/  P) S (d) -(  V/  T) P Day 22 MRs and EOSs 22.3. Transform the expressions below in terms of Cp, Cv, T, P, and V. Your answer may include absolute values of S if not associated with a derivative. (  V/  S) P

5. (a) V(  P/  S) V /T (b) TS(  V/  T) P /Cv (c) -TS/Cp (d) -S(  T/  S) P Day 22 MRs and EOSs 22.4. Transform the expressions below in terms of Cp, Cv, T, P, and V. Your answer may include absolute values of S if not associated with a derivative. (  G/  S) P

6. (a) [1/(1-b  )] (b) [1/(1-b  ) 2 ] (c) –[a  /RT] (d) [a  /RT 2 ] Day 22 MRs and EOSs 22.5. Use the vdW EOS to describe the following derivative. -T(  Z/  T) V FYI vdw EOS is: Z = [1/(1-b  )] – [a  /RT]

7. (a) -S(  T/  P) V (b) Cp(  T/  P) V (c) TS/P (d) -VS(  T/  V) P /Cp QikQiz2.1 Q2.1.1. Transform the expression below in terms of Cp, Cv, T, P, and V. Your answer may include absolute values of S if not associated with a derivative. (  A/  P) V

8. (a) V (b) V-T(  V/  T) P (c) -T(  S/  P) T +V (d) -T(  P/  T) V - P QikQiz2.1 Q2.1.2. Transform the expression below in terms of Cp, Cv, T, P, and V. Your answer may include absolute values of S if not associated with a derivative. (  H/  P) T

9. (a) RT 2 /(2*V 1.5 ) + a/(0.3*T 0.3 ) (b) (R/V 1.5 ) – 1.3a/T 2.3 (c) -1.5(R/V 2.5 ) – 1.3a/T 2.3 (d) (R/V 1.5 ) + 1.3a/T 2.3 QQ2.1 Q2.1.3. The following strange equation of state has been proposed: P = (RT/V 1.5 ) - a/T 1.3 where a is a constant. Derive an expression for (  P/  T) V

10. (a) T(1+ V(  P/  T) V /Cv ) (b) VS(  T/  V) P /Cv (c) TS/Cp (d) -VS(  T/  V) P /Cp Day 24 MRs and EOSs 24.1. Transform the expression below in terms of Cp, Cv, T, P, and V. Your answer may include absolute values of S if not associated with a derivative. (  H/  S) V

11. (a) Cv(T/P+ T(  V/  P) T /V ) (b) VS(  T/  V) P /Cv (c) TS/P (d) Cp(  T/  P ) V + [V-T(  V/  T) P ] Day 24 MRs and EOSs 24.2. Transform the expression below in terms of Cp, Cv, T, P, and V. Your answer may include absolute values of S if not associated with a derivative. (  H/  P) V

12. (a) (b) (c) (d) Day 24 MRs and EOSs 24.3. Use the PR(1976) EOS to describe the following derivative. -T(  Z/  T) V FYI: PR EOS is on P204 (Eq. 6.16-6.19)

13. (a) (b) (c) (d) Day 24 MRs and EOSs 24.4. FOR the SRK(1972) EOS: -T(  Z/  T) V = Evaluate

14. (a) Cv+ T(  P/  T) V (  V/  T) P (b) Cv+ [T(  P/  T)V –P ](  V/  T) P (c) Cp (d) (  U/  T) P + P(  V/  T) P ] Day 25 MRs and EOSs 25.1. Transform the expression below in terms of Cv, T, P, and V. Your answer may include absolute values of S if not associated with a derivative. (  H/  T) P

15. (a) (  U/  V) T - T (  S/  V) T (b) [(  P/  T) V – P] + (  P/  T) V (c) -P (d) –T (  P/  T) V Day 25 MRs and EOSs 25.2. Transform the expression below in terms of Cp, Cv, T, P, and V. Your answer may include absolute values of S if not associated with a derivative. (  A/  V) T

16. (a) (b) (c) (d) Day 26 Dep Funs 26.1. FOR the SRK EOS: Evaluate

17. (a) (b) (c) (d) Day 26 DepFuns 26.2. FOR the PR EOS: Evaluate (Hint:p602)

18. (a) (b) (c) (d) Day 26 Dep Funs 26.3. FOR the ESD EOS: where Y = exp(  /k B T)-1.06 c and q are constants Evaluate

19. (a) - V(  T/  V) P (b) PS(  T/  P) V /Cp (c) –ST/Cp (d) (  H/  S) P –T –S(  T/  S) P Day 27 QikQiz2.2 Q2.2.1. Transform the expression below in terms of Cp, Cv, T, P, and V. Your answer may include absolute values of S if not associated with a derivative. (  G/  S) P

20. (a) -T(  V/  T) P (b) [-(  V/  T) P – CpV/(ST)] -1 (c) –(ST/Cp)(  V/  T) P + V (d) -(  T/  V) P Day 27 QikQiz2.2 Q2.2.2. Transform the expression below in terms of Cp, Cv, T, P, and V. Your answer may include absolute values of S if not associated with a derivative. (  P/  S) G

21. (a) (b) (c) (d) Day 27 QQ2.2 Q2.2.3 FOR the ESD EOS: Evaluate

22. (a) (b) (c) (d) Day 27 QQ2.2 Q2.2.4 For the SAFT EOS: Derive an expression for (U-Uig)/RT

23. 28.1. Why do we write our Equation of State models as Z(T,V) or A(T,V) when what we want is V(T,P)? A.because dA = PdV – SdT is more “fundamental.” B.because pressure is a sum of forces, but density is not a sum of pressures. C.to make life difficult for poor students. D.because V(T,P) is not a function. Day 28 EOSs

24. (a) (b) (c) (d) Day 28 EOSs 28.2. FOR the ESD EOS: where Y = exp(e/kBT)-1.06 c,q are constants Evaluate

25. (a) FTFT (b) TTTF (c) TFTF (d) FFFT Day 28 EOSs 28.3.True or false ____The compressibility factor Z is always less than or equal to unity. ____The critical properties Tc and Pc are constants for a given compound. ____A steady-state flow process is one for which the velocities of all streams may be assumed negligible. ____The temperature of a gas undergoing a continuous throttling process may either increase or decrease across the throttling device, depending on conditions.

26. (a) 0.2 (b) 0.4 (c) 0.6 (d) 0.8 Day 29 HW 29.1. At 2.25$/gal, and 0.692 g/cm3, the price of gasoline in $/kg is closest to:

27. (a) 1 (b) 2 (c) 3 (d) 4 Day 29 HW 29.2. At 4$/gal, the price of propane in $/kg is closest to:

28. (a) 0.5 (b) 1.5 (c) 2.5 (d) 3.5 Day 29 HW 29.3. Referring to problem 6.21, the resulting equation of state at the given conditions has the value of Z = ___

29. (a) (b) (c) (d) Day 33 DepFuns 33.1 FOR the Scott EOS: Evaluate

30. (a) (b) (c) (d) Day 33 DepFuns 33.2 FOR the EOS: Evaluate

31. (a) high molecular weight (b) a noble gas (c) strong hydrogen bonding (d) a spherical molecule with strong hydrogen bonding Day 33 33.3 Which of the following would indicate a small acentric factor?

32. (a) 240 (b) 225 (c) 210 (d) 195 Day 33 33.4. “Boiling” is the process of transforming a liquid into a vapor. “Sublimation” is the process of transforming a solid into a vapor. For carbon dioxide, the heat of sublimation (H V -H S ) is roughly 24750 J/mole at the triple point temperature and pressure of -56.6  C and 5.27 bars. Estimate the sublimation temperature at 0.5 bar.

33. (a) 8 (b) 10 (c) -12 (d) -16 QikQiz2.3 Q2.3.1 Vapor ethylene oxide is compressed from 25  C and 1 bar to 125  C and 20 bar. The change in entropy (J/mol-K) is:

34. (a) 425 (b) 450 (c) 470 (d) 500 QikQiz2.3 Q2.3.2. Determine the work (kW) required to continuously compress reversibly and adiabatically 0.5kg/min of ethylene oxide from 25  C and 1 bar to 20 bar. The temperature (K) exiting the compressor is:

35. (a) 1.8 (b) 2.0 (c) 200 (d) 9000 QikQiz2.3 Q2.3.3. Determine the work (kW) required to continuously compress reversibly and adiabatically 0.5kg/min of ethylene oxide (MW=40) from 25  C and 1 bar to 20 bar.

36. (a) 45 (b) 35 (c) 25 (d) 15 QikQiz2.3 Q2.3.4. Ethylene oxide (MW=40) enters a throttle as saturated liquid at 2MPa and exits at 1bar. Determine the quality (%) at the exit.

37. (a) (b) (c) (d) Day 33 HW Ch 7&8 33.1 FOR the SRK EOS: Evaluate

38. (a) –ln(1-b  ) - a  /RT1.7 + Z – 1 - lnZ (b) -2ln(1-2b  ) - a  /RT 1.7 + Z – 1 - lnZ (c) -2ln(1-2b  ) + 1.7a  /RT 2.7 + Z – 1 - lnZ (d) -4ln(1-2b  ) - a/RT 1.7 + Z – 1 - lnZ QikQiz2.4 Q2.4.1. Derive the simplest form of the Gibbs energy departure function for the following equation of state: Z = 1 + 4b  /(1-2b  ) - a  /RT 1.7

39. (a) 1 (b) 2 (c) 3 (d) 4 QikQiz2.4 Q2.4.2. Estimate the vapor pressure (bars) of n-butane at T=40  C.

40. (a) 300 (b) 325 (c) 350 (d) 375 QikQiz2.4 Q2.4.3. Estimate the saturation temperature (K) of n- butane at P=20bars.

41. (a) 240 (b) 225 (c) 210 (d) 195 QikQiz2.4 Q2.4.4. “Boiling” is the process of transforming a liquid into a vapor. “Sublimation” is the process of transforming a solid into a vapor. For carbon dioxide, the heat of sublimation (H V -H S ) is roughly 24750 J/mole at the triple point temperature and pressure of -56.6  C and 5.27 bars. Estimate the sublimation temperature at 0.5 bar.

42. (a) (b) (c) (d) Qq2.5.1. FOR the Scott EOS: Evaluate QikQiz2.5

43. (a) (b) (c) (d) Qq2.5.2. FOR the EOS: Evaluate QikQiz2.5

44. (a) 0.3 (b) 0.4 (c) 0.5 (d) 0.6 QikQiz2.5 Q2.5.3. A power cycle is to run on bromine operating at 0.1MPa in the condenser and 6MPa in the boiler. Estimate the Carnot efficiency.

45. (a) 18 (b) 12 (c) 6 (d) 3 QikQiz2.5 Q2.5.4. A Rankine cycle is to operate on bromine operating at 0.1MPa in the condenser and 6MPa in the boiler. Estimate the turbine work (kJ/mol).

46. (a) 0.3 (b) 0.4 (c) 0.5 (d) 0.6 QikQiz2.5 Q2.5.5. A Rankine cycle is to operate on bromine operating at 0.1MPa in the condenser and 6MPa in the boiler. Estimate the Rankine efficiency.

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