Thermo Quals

8/18/2019 Thermo Quals

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Thermo Questions

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Pr oblem 8

A binary liqui d system in equilibrium with its vapor is described by the modified Raoult’s law. Theactivity coefficients depend on composition as follows:

212

221

ln

ln

Ax

Ax

Experimental data for a particular liquid mixture are as follows:

mol mol y

mol mol x

kPaC P

kPaC P

C T

o sat

o sat

o

/44.0

/32.0

7.57)110(

2.52)110(

110

1

1

2

1

(a) Identify the more volatile species.(b) Calculate the value of parameter A.(c) Calculate the pressure of the system in kPa.(d) Evaluate whether the system can form an azeotrope at this particular temperature. If so, calculate the

pressure and composition at the azeotrope.Assume ideal behavior of the vapor.


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Thermo Questions

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May 2011

Pr oblem 1

(1) Answer the questions below based on the phase diagram shown below for a mixture ofcomponents 1 and 2. y 1 = mole fraction component 1.

(a) At T = 60 ⁰ C what are the compositions of the phases that form?(b) At T = 60 ⁰ C, consider the phase rich in species 1, L’. If γ 1’ in this phase is ~1, then what is

γ1” in the other phase?

(c) Over what range of T and z 1 (overall mole fraction) can one form a vapor in equilibrium witha

Liquid rich in component 2?

(d) A hot mixture at y 1 = 0.4 is cooled to T = 76 ⁰ C.

What kinds of phases and how many of each form?

What are the compositions of each phase?

What are γ1’ and γ1” at this condition?

50

60

70

80

90

100

105

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

y1

T ( ⁰ C)

VAPOR

LIQUID


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Thermo Questions

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January 2011

Pr oblem 3

Two pure liquids (species A and B) are mixed isothermally at 25ºC in equimolar amounts and kept incontact with air at 1 bar. The solubility of air in mixtures of A and B is negligible at all compositions.The pure components have the following properties at 25ºC: PAsat = 0.6 bar, PBsat = 0.3 bar. Inaddition, the following is known about the mixture properties:

• The heat of mixing of the two components at 25ºC is -1 kJ/mol for a 50/50 molar mixture.• The excess entropy at 25ºC is - 1 J/mol•K for a 50/50 molar mixture.

a) Assuming that the mixture can be represented by the simple Margules model

the equimolar mixture.

b) Calculate the concentration (mole fraction) of A and B in the air that is in equilibriumwith the equimolar mixture at 25ºC.

Pr oblem 4

Air from the compressor of a jet engine is being used to air condition a plane’s passenger cabin. The air,at 1 bar and 38 °C, is expanded through a turbine to the cabin pressure of 0.8 bar, used to cool the cabin,and finally exhausted. Three thousand joules/sec must be removed from the cabin to maintain thetemperature at 22 °C. Determine:

(a) at what rate (in mol/sec) air enters the turbine

(b) how much work (in J/sec) the turbine performs

(c) State any assumptions that you make.


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Thermo Questions

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May 2010

Pr oblem 3

Pr oblem 6

Pr oblem 8


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Thermo Questions

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January 2010

Pr oblem 1

Pr oblem 4


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Thermo Questions

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May 2009

Pr oblem 3

An ideal gas is compressed adiabatically in a steady-state process. This process has 87% efficiency. Thefollowing inlet and outlet conditions are known:

Inlet: Pin = 0.1 MPa, Tin = 25 ° COutlet: Pout = 0.4 MPa

Assume that the gas is diatomic, such that cv = 5/2 R and cp = 7/2 R.(a) What is the temperature Tout in the outlet stream?(b) What is the entropy change between the two streams?

Pr oblem 7

(1) Answer the questions below based on the phase diagram shown below for a mixture of components 1 and2. x 1 = mole fraction component 1.

(a) At P = 3 bar, what are the compositions of the phases that form?Phase L’ has x 1’=0.12 and Phase L” has x 1”=0.83(b) At P = 3 bar, consider the phase rich in species 2, L’. If γ 2’ in this phase is ~1, then what is γ 2” in theother phase?Equilibrium determined by two equations: γ 1’x1’=γ 1”x1” and γ 2’x2’=γ 2”x2”γ2” = γ 2’x2’/x2” = (1) (1 -0.12) / (1-0.83) = 0.88/0.17 = 5.18(c) Over what range of P and z 1 (overall mole fraction) can one form a Vapor in equilibrium with a Liquidrich in component 1?Read from the chart the limits of the coexistence region V- L” labeled below:0.8 < P < 2 bar and 0.44 < z1 < 1.0

(d) A mixture at x 1 = 0.3 is compressed to P = 2.0 bar.

What kinds of phases form? Vapor + two liquid phases, L’ and L”What are the compositions of each phase? x 1’= 0.18, y 1 = 0.44, x 1” = 0.83What are γ1’ and γ1” at this condition?Py1=γ1’x1’P1* = γ 1”x1”P1*P1* = 0.8 bar from the chart, thus γ 1’= Py 1 / x1’P1*= 2(0.44)/((0.18)(0.8)) = 6.11

And γ1”= Py

1/ x

1”P

1*=2(0.44)/((0.83)(0.8))= 1.33

MISSING GRAPH!!


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Thermo Questions

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January 2009

Pr oblem 1

One mole of an ideal gas at 350o

C and 1030kPa is expanded in a turbine. The exhaust pressure isatmospheric (103kPa). What is the lowest possible temperature of the exhaust? How much work isobtained? Assume the heat capacity (C p = 3.5R) and negligible heat transfer to the surroundings. R =8.314 J mol -1 K -1

Pr oblem 4

An ideal equimolar liquid solution of hexane and heptane is flashed isothermally at 80 oC. The product ishalf vapor and half liquid; calculate the pressure (in torr) and composition of each stream. The vapor

pressures are P sat hexane = 1082 torr, P sat heptane = 388 torr.

Pr oblem 8

A piston-cylinder device contains an ideal gas. Within the cylinder, the gas is at T = 300 K, P = 200 kPa,and V = 1 m 3. The mass of the piston is 1 kg and the acceleration due to gravity today is 10 m/s 2. The

piston is held in place by a mechanical stopper (stopper#1).

The whole piston-cylinder device has been placed in a rigid vacuum chamber and the vacuum chamberwas evacuated so that P ~ 0 Pa. (The gas is still inside the piston cylinder though). See the figure below.

Stopper #1 is removed and the piston is forced upward by the pressure inside the piston cylinder. The piston rises one meter until it hits stopper #2, at which point it stops. The volume inside the piston-cylinder is now 2 m 3.

What is the final temperature and pressure inside the piston-cylinder?


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Thermo Questions

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May 2008Pr oblem 1

A process has been proposed whereby 1.5 kmol of an ideal gas (Cp = 30 kJ/kmol-K) is taken from P =10 bar and T = 300 K to P = 1 bar and T = 500 K in a closed system. During the process the systemdoes work, and receives 5000 kJ of heat reversibly from the surroundings at 300 K.

a. How much work would need to be done by the system on the surroundings? b. Is this process possible?c. Would it be possible for the gas to undergo the same change in state adiabatically? Explain.d. Would it be possible for the gas to return to its original state adiabatically? Explain.

Pr oblem 2

How does the internal energy of a fluid vary with the volume at constant temperature, in terms of P-V-T properties only?

a. In the general case b. For an ideal gas

c. For a van der Waals fluid, RT bvva

p

2

January 2008

Pr oblem 1

A piston-cylinder device initially contains 0.50 m 3 of an ideal gas at 150 kPa and 20°C. The gas issubjected to a constant external pressure of 400 kPa and compressed in an isothermal process. Assumethe surroundings are at 20°C. Take C P = 2.5R and assume the ideal gas model holds.

a. Determine the heat transfer (in kJ) during the process. b. What is the entropy change of the system, surroundings, and universe?c. Is the process reversible, irreversible, or impossible?


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Thermo Questions

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Pr oblem 3

A tank is used to heat oil by saturated steam, which is condensing in steam coils at 40.0 psia. Oil flowsin and out of the tank at a rate of 1018.0 lb m/h. The tank, which is perfectly mixed by a stirrer, contains5000 lb m of oil initially at 60

°

F. The temperature of the inflowing oil is also 60 ° F. The rate of heat

transfer from th e steam to the oil is given by Newton’s heating law,

Q = U(T steam - T oil )

Where Q is the rate of heat transfer in Btu/h and U is an overall heat transfer coefficient. Calculate thetime in hours it will take for the discharge from the tank to rise from 60 ° F to 90 ° F and the maximumtemperature that can be achieved in the tank.

Additional data:

Power of stirrer motor: 1.0 hp; 75% of this power is delivered to the oil.

U= 291 Btu/(H ·°

F)C p,oil = 0.5 Btu/(lbm · ° F)1 hp = 2547 Btu/hWater saturation temperature at 40 psia is 130.7 ° C = 267.2 ° F

Pr oblem 6

A sealed vessel contains water and air (which consists of oxygen and nitrogen in the ratio 1:4) at 25 ° Cand 1 bar. Calculate the mole fraction of water vapor, and the solubility of oxygen and nitrogen inwater. Henry’s constants for oxygen and nitrogen in water at 25 ° C are 43500 bar and 84800 bar,respectively. The vapor pressure of water at 25

°

C is 0.0317 bar.

May 2007Pr oblem 3

The following data are available for water (1) + formic acid (2) mixtures at 45 C:γ1 = 0.49 ; γ 2 = 0.74. Calculate the amount of heat added or removed when an equimolar mixture of water

and formic acid is formed from its components at 45 C. You may use the Margules equation as follows:

ln γ 1 = x 22 [A12 + 2 (A 21 - A 12 ) x 1]


11/26

Thermo Questions

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Pr oblem 5

A 1 m 3 rigid box contains 1 mole of nitrogen at T=300 K (ideal gas with C p =30 J/(mole K), and C V=20 J/(moleK), R=8.314 J/(mole K). The box is connected to a high-pressure nitrogen gas line containing nitrogen atP=200,000 Pa and T=300 K via a valve. The valve is opened and one mole of nitrogen flows through the valveinto the box. The conditions of the nitrogen gas in the high-pressure line do not change during the filling. Thevalve is then closed. Heat is allowed to flow between the box and the surroundings (which are also at 300 K) sothat the box returns to 300 K. How much heat is exchanged between the box and the surroundings? Nitrogen

behaves like an ideal gas under all conditions.

January 2007

Pr oblem 3

Consider gas flowing out of a small hole in a tank, at a constant rate m [e.g. kg/s].

Neglect potential and kinetic energy. Assume that the gas is ideal and use a reference temperature of T r for allthermodynamic quantities. Assume the tank is well insulated.

The initial mass is m0, and the initial temperature is T 0. Compute the temperature in the tank as a function of time.

(1) Derive the transient energy balance for the tank, in terms of temperature T in the tank. (assuming that0)( t mt m so that the tank is not empty).

(2) Consider very early behavior, such that t mt m )( so that t m can be neglected relative to m0. Solve thetransient balance for T(t) .

m

.


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Thermo Questions

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Pr oblem 5

A liquid mixture of cyclohexanone (1) and phenol (2) for which x 1= 0.6, is in equilibrium with its vapor at144 oC. Determine the equilibrium pressure, P, and the composition of the vapor, y 1, from the followinginformation:

(1) Assume the composition dependence of G E (Excess Gibbs free energy) is given by an equation of the formGE/RT = Bx 1x2, where B is a function of temperature only.

(2) At 144 oC, P 1sat = 75.20 kPa and P 2sat = 31.66kPa.(3) The system forms an azeotrope at 144 oC for which x 1azeo = y 1azeo = 0.294.

May 2006

Pr oblem 1

Solid sodium carbonate monohydrate loses water vapor upon heating to form anhydrous sodiumcarbonate. The equilibrium water vapor pressure above the solid (which behaves like an ideal gas) has

been measured as a function of temperature, as follows:

Log 10 (Po) = 7.9 – (3000/T)(where P 0 is the partial pressure of water in bar and T is in degrees K)

What is the standard Gibbs Energy change for the reaction at 600 K, based only on this information? Na 2CO 3*H 2O → Na 2CO 3 + H 2O

Pr oblem 5

Air (treated as ideal gas) is contained in a vertical cylinder at a pressure of 20 bar. The pressure is

imposed by a weight on a frictionless piston, so that the pressure remains constant. The initial volume of

the air in the cylinder is 0.05 m 3, the specific internal energy of the air U = 89.14 kJ/kg, specific volume

V = 20 m 3/kg. The valve is opened to allow 0.0015 kg air flowing from a large tank to the cylinder, and

then it is closed. The specific enthalpy of the air in the tank is 229.6 kJ/kg During the process the

pressure P, specific internal energy U, and specific volume V remain constant at their initial values.

Assume the kinetic and potential energies are negligible. In this process,

a. What is the final volume of the vertical cylinder?

b. How much work is done?

c. How much heat is transferred?


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Thermo Questions

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Pr oblem 7

An ideal liquid solution of benzene, toluene, and o-xylene is in equilibrium with its vapor at 100ºC; noother substances are present. The liquid composition (mole fraction) and vapor pressures in torr (mmHg) at this temperature are given below. What is the total pressure and vapor composition?

x P sat , torrBenzene 0.25 1340Toluene 0.35 560o-Xylene 0.40 210

a) Total Pressure: P = _________________torr b) Composition: y Benzene = ___________

yToluene = ___________yXylene = ____________

January 2006

Pr oblem 1

A storage vessel is filled with a liquid mixture initially with the following composition: 50 mol %toluene, 45 mol % styrene and the balance liquid iodine (assumed to be nonvolatile). Nitrogen is

bubbled through this liquid at a temperature of 115 °C. The N 2 flow rate is 90 moles/min. The gasleaving the bubbler is saturated with toluene and styrene vapors and initially contains 25 mol % N 2.

(a) What is the initial pressure of the vessel?

_________mm Hg

(b) What is the initial mole fraction of toluene in the vapor phase?

________

(c) What is the initial molar flow rate at which toluene leaves the bubbler?

_________ mol/min

Vapor pressure data:

Toluene: P*(115 °C) = 859 mmHgStyrene: P*(115 °C) = 315 mmHg


14/26

Thermo Questions

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Pr oblem 4

A fish tank (30 cm wide x 50 cm long x 50 cm deep) is used to keep goldfish at 20°C. Each goldfishneeds 10 -4 g of O 2 per hour to survive. The Henry's law constant for oxygen in water is 40,000 bars at20°C. The viscosity of water at 20°C is 1 cp. It may be further assumed that a minimum concentration of

10 -7 mol O 2/cm 3 needs to be maintained in water. The oxygen transfer from air to water is controlled bymolecular diffusion of oxygen through the top layer (0.5 cm thick) of water. This layer may be assumedstagnant, and water below this layer is well-mixed by the movement of goldfish. The diffusivity ofoxygen in water at 20°C is 2x10 -5 cm 2/s. Estimate the number of goldfish that can be sustained in thetank.

May 2005

Pr oblem 1

A car advertisement states that its turbocharger compresses atmospheric intake air to 2 bar. Thecompressor is driven by the exhaust gas by use of a turbine (see figure below). You skepticism leads youto get more information about the turbocharger.

The compressor operates isothermally and reversibly at 320 K, compressing intake air at 320 K from 1 bar to 2 bar. The intake air flowrate is 2 mol/s. Assume the intake air is ideal.

The turbine operates isobarically at the exhaust pressure of 1.5 bar. The exhaust gas flows at 2.5 mol/s,enters the turbine at 550 K, and exits the turbine at 400 K. Assume the exhaust gas is ideal.

Using this information, perform a thermodynamic analysis to decide if the turbocharger can operate asstated.

HINTS: Assume all heat is lost reversible at the temperature of the compressor, so that the associated

entropy , where is heat flow and T is temperature. For isobaric expansion of an ideal gas, the change in entropy,

, where is the mass of gas and is the gas constant.


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Thermo Questions

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Pr oblem 2

The bubble point temperature of a liquid mixture of A and B containing 4.0 mole% of A is 92.7 oC at1.012 bar. At 92.7 oC, the vapor pressure of pure A is 0.427 bar and the vapor pressure of pure B is 0.784

bar.

a. Assume that the activity coefficient of B equals 1.0 in the liquid mixture containing 4.0 mole% Aand 96 mole% B. You may also assume that the vapor phase follows ideal gas behavior.i. What is the composition of the vapor in equilibrium with the liquid mixture containing 4.0

mole% A and 96 mole% B? ii. What is the activity coefficient of A?

b. At 92.7 oC, the maximum amount of A that can be dissolved in an A-B mixture is 4.0 mole percent.When larger amounts of A are present, a second liquid phase, containing 40.0 mole percent Aappears. What are the activity coefficients for A and B in this second phase?

January 2005

Pr oblem 1

A real gas is contained in an insulated piston cylinder with the following initial conditions:

Volume = 1 cubic footTemperature = 45 oCPressure = 0.6 psia

The piston initially held with a latch. The surrounding pressure is held at a contact value of 14 psia. Findthe heat transf erred (Q) and the enthalpy change (ΔH) between the time the latch is removed and thetime the piston comes to rest. Express your answer using energy units of ft-lb f .

Pr oblem 2

Consider the following two vapor-liquid systems.a. Vapor-liquid equilibrium for the system containing components A and B at temperature of 80 oC

shows that component B obeys Henry’s law in the range 0 < x B < 0.02, where x B is theliquid phase mole f raction of B. The Henry’s law constant is 500mmHg/(mole fraction B). Thesaturation vapor pressure of pure A at 80 oC is P A* = 1,000 mmHg. For x B = 0.01, calculate the (i)equilibrium pressure and (ii) molar composition of A and B in the vapor phase.

b. Assuming ideal solution behavior, calculate the (i) equilibrium pressure and (ii) molarcomposition of the vapor phase in equilibrium with a solution of carbon tetrachloride (CCl 4) andcyclohexane at 40 oC that has a CCl 4 mole fraction, x CCl4 = 0.475. The saturation vapor

pressures at 40 oC of pure CCl 4 and cyclosexane are P CCl4 * = 213.34 mmHg and P cyclohexane * =184.61 mmHg, respectively.


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Thermo Questions

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May 2004

Pr oblem 1

A Fast talking salesperson comes to your door, offering to sell his patent rights to marvelous invention.He brings out the mysterious box and claims that it can take an inlet stream at 2 kg/s of an ideal gas at4 bar and 50 oC and convert it to two outlet streams. One outlet stream flows at 0.5 kg/s and is at 1 barand -10 oC. The second outlet stream exits at 1.5 kg/s and is at 1 bar and 70 oC. Will this device work?Justify your response with quantitative calculations.

Pr oblem 2


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Thermo Questions

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January 2004

Pr oblem 1

Pr oblem 2

May 2003

Pr oblem 1


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Thermo Questions

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Pr oblem 2

Pr oblem 5


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Thermo Questions

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January 2003

Pr oblem 1

Pr oblem 3


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Thermo Questions

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Pr oblem 6

May 2002

Pr oblem 1


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Thermo Questions

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Pr oblem 6

January 2002

Pr oblem 5


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Thermo Questions

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Pr oblem 3

In order to air condition a lecture hall to 21 oC, 7.5 x 10 5 kJ of heat must be removed from this hall perhour. An inventor claims to have invented a device that neither requires nor generates work, but canaccomplish the required air conditioning by supplying 1 x 10 6 kJ/hr to the device at 150 oC, and by

having a heat reservoir available at 38oC.

a. Should you, as the lead engineer on the project, purchase this device? Quantitatively justify youranswer

b. What is the minimum temperature that the lecture hall could reach using this device under theabove conditions?

Pr oblem 1


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Thermo Questions

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May 2001

Pr oblem 2

Pr oblem 3


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Thermo Questions

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January 2001

Pr oblem 1

Pr oblem 6


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Thermo Questions

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Pr oblem 7


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Thermo Questions

January 2000

Pr oblem 3

Pr oblem 7

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