ConcepTests in Chemical Engineering ThermodynamicsUnit 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

(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

(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

(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

(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

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

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]

(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

(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

(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

QQ2.1

Q2.1.3. The following strange equation of state has been proposed: P = (RT/V1.5) - a/T1.3

where a is a constant. Derive an expression for (P/T)V

(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

(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

(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)

2 2

1

1 2 ( )

a da b

bRT bRT dT b b

2

1

1 2 ( )

a da b

bRT bR dT b b

21

1 2 ( )c ra Ta b

bRT a b b

21 2 ( )c ra T b

bRT b b

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

Day 24 MRs and EOSs

24.4. FOR the SRK(1972) EOS:

-T(Z/T)V = Evaluate

2( )1

1c ra Ta b

bRT a b

1 ln 1c ra Tab

bRT a

ln 1c ra Tb

bRT

11

c ra Ta b

bRT a b

0

( )b

V

Z d bT

T b

20.5( )1 ln

1c ra Ta b

bRT a b

(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

(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

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

Day 26 Dep Funs

26.1. FOR the SRK EOS:

Evaluate

ln(1 ) ln(1 )a

b bbRT

ln(1 ) ln(1 )a

b bbRT

2

ln(1 )ln(1 )

b ab

b b RT

11 1

b a bZ

b bRT b

0

( )( 1)

bd b

Zb

20.5( )ln(1 ) ln

1

a bb

bRT b

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

Day 26 DepFuns

26.2. FOR the PR EOS:

Evaluate(Hint:p602)

ln(1 ) ln(1 )a

b bbRT

1 2.414ln(1 ) ln

1 0.414

a bb

bRT b

2 8ln(1 ) ln

8 2 8

a bb

bRT b

211 1 2 ( )

b a bZ

b bRT b b

0

( )( 1)

bd b

Zb

1ln(1 ) arctan

8 2

a bb

bRT

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

Day 26 Dep Funs26.3. FOR the ESD EOS:where Y = exp(/kBT)-1.06c and q are constants

Evaluate

4 ln(1 1.9 ) 9.5ln(1 1.8 )

1.9 1.8

c b qYYb

4 ln(1 1.9 ) 9.5ln(1 1.8 )

1.9 1.8

c b qYb

4 ln(1 1.9 ) 9.5ln(1 1.8 )

1.9 1.8

c b qYYb

4 9.511 1.9 1 1.8

cb qYbZ

b Yb

4 ln(1 1.9 ) 9.5 ln(1 1.8 )c b q Yb

0

( )( 1)

bd b

Zb

(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

(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

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

Day 27 QQ2.2

Q2.2.3 FOR the ESD EOS:

Evaluate

ln(1 1.9 )b

4ln(1 1.9 )b

4ln(1 1.9 )

1.9

b

411 1.9

HS bZ

b

0

( )( 1)

bHS d bZ

b

4ln(1 1.9 )b

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

Day 27 QQ2.2

Q2.2.4 For the SAFT EOS:

Derive an expression for (U-Uig)/RT

2

3 1 2

(1 )

A A

b T T

2

1( ) 2( )3ln(1 )

igA A A b A bb

RT T T

2

3 1 2

(1 )

A A

b T T

2

1 22

A A

T T

2

1 2A A

T T

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

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

Day 28 EOSs28.2. FOR the ESD EOS:where Y = exp(e/kBT)-1.06c,q are constants

Evaluate

4 ln(1 1.9 ) 9.5ln(1 1.8 )

1.9 1.8

c b qYYb

4 ln(1 1.9 ) 9.5ln(1 1.8 )

1.9 1.8

c b qYb

4 ln(1 1.9 ) 9.5ln(1 1.8 )

1.9 1.8

c b qYYb

4 9.511 1.9 1 1.8

cb qYbZ

b Yb

,( )T VA Aig

RT

4 ln(1 1.9 ) 9.5 ln(1 1.8 )c b q Yb

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

Day 28 EOSs28.3.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) 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:

(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:

(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 = ___

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

Day 33 DepFuns

33.1 FOR the Scott EOS:

Evaluate

2ln(1 2 ) 1 ln( )b Z Z

2ln(1 2 ) 1 ln( )b Z Z

4ln(1 2 ) 1 ln( )b Z Z

1 2

1 2

bZ

b

( )igG G

RT

1 2ln 1 ln( )1 2

bZ Z

b

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

Day 33 DepFuns

33.2 FOR the EOS:

Evaluate

2ln(1 )b

1

ab

b

2(2 )

2 1

a b b

b

31

1

abZ

b

,( )ig T VA A

RT

2/ 2

1

a

b

(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?

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

QikQiz2.3

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) 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 25C and 1 bar to 20 bar. The temperature (K) exiting the compressor is:

(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 25C and 1 bar to 20 bar.

(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.

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

Day 33 HW Ch 7&8

33.1 FOR the SRK EOS:

Evaluate

1 ln 1 ln( )c ra TaZ b Z

bRT bRT

1 ln 1c ra TaZ b

bRT bRT

,( )ig T PH H

RT

1

11

c ra TaZ

bRT bRT b

21

11

c ra TaZ

bRT bRT b

(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

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/RT1.7

(a) 1(b) 2(c) 3(d) 4

QikQiz2.4

Q2.4.2. Estimate the vapor pressure (bars) of n-butane at T=40C.

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

QikQiz2.4

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

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

Qq2.5.1. FOR the Scott EOS:

Evaluate

2ln(1 2 ) 1 ln( )b Z Z

2ln(1 2 ) 1 ln( )b Z Z

4ln(1 2 ) 1 ln( )b Z Z

1 2

1 2

bZ

b

( )igG G

RT

1 2ln 1 ln( )1 2

bZ Z

b

QikQiz2.5

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

Qq2.5.2. FOR the EOS:

Evaluate

2ln(1 )b

1

ab

b

2(2 )

2 1

a b b

b

31

1

abZ

b

,( )ig T VA A

RT

2/ 2

1

a

b

QikQiz2.5

(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.

(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).

(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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