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(a) ( P / V ) S (b) ( T / V ) U (c) ( U / T ) V (d) ( P / T ) V

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

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

(a) (P/V)S (b) (T/V)U (c) (U/T)V (d) (P/T)V

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

(a) Cv(T/P)V/T (b) (T/V)U(c) (U/T)V(d) (P/T)V

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

(a) Cv(T/P)V/T (b) T(V/T)P/Cp(c) (T/P)S(d) -(V/T)P

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

(a) V(P/S)V/T(b) TS(V/T)P/Cv(c) -TS/Cp(d) -S(T/S)P

22.5. Use the vdW EOS to describe the following derivative. -T(Z/T)VFYI vdw EOS is: Z = [1/(1-br)] – [ar/RT]

(a) [1/(1-br)] (b) [1/(1-br)2] (c) –[ar/RT](d) [ar/RT2]

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

(a) -S(T/P)V(b) Cp(T/P)V(c) TS/P(d) -VS(T/V)P /Cp

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

(a) V(b) V-T(V/T)P(c) -T(S/P)T+V(d) -T(P/T)V - P

Q2.1.3. The following strange equation of state has been proposed: P = (RT/V1.5) - a/T1.3where a is a constant. Derive an expression for (P/T)V

(a) RT2/(2*V1.5) + a/(0.3*T0.3)(b) (R/V1.5) – 1.3a/T2.3(c) -1.5(R/V2.5) – 1.3a/T2.3(d) (R/V1.5) + 1.3a/T2.3

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

(a) T(1+ V(P/T)V/Cv )(b) VS(T/V)P/Cv(c) TS/Cp(d) -VS(T/V)P /Cp

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

(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]

24.3. Use the PR(1976) EOS to describe the following derivative. -T(Z/T)VFYI: PR EOS is on P204 (Eq. 6.16-6.19)

(a)(b) (c) (d)

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

(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]

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

(a) (U/V)T - T (S/V)T(b) [(P/T)V – P] + (P/T)V(c) -P(d) –T (P/T)V

26.3. FOR the ESD EOS:where Y = exp(e/kBT)-1.06c and q are constants Evaluate

(a)(b) (c) (d)

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

(a) - V(T/V)P(b) PS(T/P)V/Cp(c) –ST/Cp(d) (H/S)P –T –S(T/S)P

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

(a) -T(V/T)P(b) [-(V/T)P – CpV/(ST)]-1(c) –(ST/Cp)(V/T)P + V(d) -(T/V)P

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)?

Day 28 EOSs

- because dA = PdV – SdT is more “fundamental.”
- because pressure is a sum of forces, but density is not a sum of pressures.
- to make life difficult for poor students.
- because V(T,P) is not a function.

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.

(a) FTFT(b) TTTF (c) TFTF(d) FFFT

29.1. At 2.25$/gal, and 0.692 g/cm3, the price of gasoline in $/kg is closest to:

(a) 0.2(b) 0.4(c) 0.6(d) 0.8

29.3. Referring to problem 6.21, the resulting equation of state at the given conditions has the value of Z = ___

(a) 0.5(b) 1.5(c) 2.5(d) 3.5

33.3 Which of the following would indicate a small acentric factor?

(a) high molecular weight(b) a noble gas(c) strong hydrogen bonding(d) a spherical molecule with strong hydrogen bonding

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 (HV-HS) is roughly 24750 J/mole at the triple point temperature and pressure of -56.6C and 5.27 bars. Estimate the sublimation temperature at 0.5 bar.

(a) 240(b) 225(c) 210(d) 195

Q2.3.1 Vapor ethylene oxide is compressed from 25C and 1 bar to 125C and 20 bar. The change in entropy (J/mol-K) is:

(a) 8(b) 10(c) -12(d) -16

Q2.3.2. Determine the work (kW) required to continuously compress reversibly and adiabatically 0.5kg/min of ethylene oxide from 25C and 1 bar to 20 bar. The temperature (K) exiting the compressor is:

(a) 425(b) 450(c) 470(d) 500

Q2.3.3. Determine the work (kW) required to continuously compress reversibly and adiabatically 0.5kg/min of ethylene oxide (MW=40) from 25C and 1 bar to 20 bar.

(a) 1.8(b) 2.0(c) 200(d) 9000

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.

(a) 45(b) 35(c) 25(d) 15

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/RT1.7

(a) –ln(1-b)- a/RT1.7 + Z – 1 - lnZ(b) -2ln(1-2b)- a/RT1.7 + Z – 1 - lnZ(c) -2ln(1-2b) + 1.7a/RT2.7 + Z – 1 - lnZ(d) -4ln(1-2b)- a/RT1.7 + Z – 1 - lnZ

Q2.4.3. Estimate the saturation temperature (K) of n-butane at P=20bars.

(a) 300(b) 325(c) 350(d) 375

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 (HV-HS) is roughly 24750 J/mole at the triple point temperature and pressure of -56.6C and 5.27 bars. Estimate the sublimation temperature at 0.5 bar.

(a) 240(b) 225(c) 210(d) 195

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.

(a) 0.3(b) 0.4(c) 0.5(d) 0.6

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).

(a) 18(b) 12(c) 6(d) 3

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.

(a) 0.3(b) 0.4(c) 0.5(d) 0.6

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