##### Document Text Contents

Page 1

Code No:220802

II.B.Tech II-Semester. Supplementary Examinations. January,2003

CHEMICAL ENGINEERING THERMODYNAMICS

(Chemical Engineering)

Time: 3 hours. Max.Marks:80

Answer any FIVE questions

All questions carry equal marks.

---

1. Explain the following and give two examples of each

a) (i) Extensive and Intensive properties.

(ii) Reversible and irreversible processes.

(iii) State function and path function.

b) Water flows through a horizontal coil heated from the outside by high temperature

flue gases. As it passes through the coil, the water changes state from 2 atm

(202.66 KPa) and 180o F (82.2oC) to 1 atm (101.33 KPa) and 250o F (121.1oC).

Its entering velocity is 10 ft/sec (3.05 m/s) and its exit velocity is 600 ft/s

(182.9 m/s) Determine the heat transferred through the coil per unit mass of

water. Enthalpies of the inlet and outlet water streams are

inlet = 148 Btu/lbm (344.2 KJ/kg)

output = 1168.8 Btu/lbm (2718.5 KJ/kg)

2. a) Explain the application of cubic equations of state.

b) Determine the molar volume of n-butane at 510oK and 25 bar by each of the

following.

(i) The ideal gas equation

(ii) The generalized compressibility factor correlation

(iii) The generalized virial - coefficient correlation.

3. a) If 10 moles of ethylene is heated from 200oC to 1000oC in a steady flow process

at approximately atmospheric pressure. What is its entropy change. Give that,

A = 1.424; B = 14.394 x 10-3; C = -4.392 x 10-6; D = 0.

b) One mole of an ideal gas is compressed isothermally but irreversibly at 400 K

from 3 bar to 7 bar in a piston cylinder device. The work required is 35% greater

than the work of irreversible isothermal compression. The heat transferred from

the gas during compression flows to a heat reservoir at 300 K. Calculate the

entropy changes of gas, reservoir and ∆ S total.

4. a) For acetone at 20oC and 1 bar β = 1.487x10-3 / 0C , K = 62X10-6/bar,

V = 1.287

gm

cm3

Find (i) The value of

vT

P

∂

∂

(ii) The pressure generated when acetone is heated at constant volume from

20oC and 1 bar to 30oC.

(iii) The volume change when acetone is changed from 20oC and 1 bar to 0oC

and 10 bar

Contd…….2

Set No:

1

Page 2

Code No:220802 -2- Set No:1

b) Show that

(i)

+

∂

∂

=

∂

∂

pTH C

T

P

V

P

V

PP C

V

T

V

−

∂

∂ 2

PT

V

∂

∂

(ii) S

OTPT

PC

T

A

v

v

s

−

∂

=

∂

∂

/(

5. a) Derive Maxwell’s equations, explain their importance.

b) Estimate VR, HR and SR for steam at 200oC and 1400 kpa by using generalized

correlations. Given that TC = 647.3 K, PC = 220.5 bar, VC = 56 cm3/mol

W = 0.344.

6. Calculate Z and V for methanol vapour at 200oC and 10 bar by the following

equations.

a) A truncated virial equation

2

1

V

C

V

B

RT

PV

Z ++== with the following values of

virial coefficients, B = -219 cm3/mol, C = -17,300 cm6/mol.

b) The truncated virial equation

RT

BP

RT

PV

Z +== 1 with a value of B from the

generalized pidzer correlation.

c) The Red lich -Kwong equation with estimates of a and b given, Tc = 512.6K,

Pc = 81 bar W = 0.564.

7. a) Explain about the variations of heat capacity of a substance with temperature.

b) How much heat would be absorbed or released from hydrogenation of acetylene

to ethane at standard conditions.

C2 H2 (g) + 2H2 (g) C2 H6(g)

(i) Use heat of combustion data

(ii) Use heat of formation data.

Combustion data at 25oC : C2 H2 : ∆HoC = -310620 cal/gm

C2 H6 : ∆HoC = -372820 cal/gm

H2 : ∆HoC = -68317 cal/gm

Heat of formation data at 25oC:

C2 H2 : ∆Hƒ = 54194 cal/g.mole

C2 H6 : ∆Hƒ = -20236 cal/g.mole

8. Write short notes on any two of the following.

(i) Phase rule and criterion for equilibrium.

(ii) Heat effects of Industrial reactions.

(iii) Thermodynamic properties of an ideal bas.

@@@@@

Page 3

Code No:220802

II.B.Tech II-Semester. Supplementary Examinations. January,2003

CHEMICAL ENGINEERING THERMODYNAMICS

(Chemical Engineering)

Time: 3 hours. Max.Marks:80

Answer any FIVE questions

All questions carry equal marks.

---

1. a) State the first law of thermodynamics. Obtain an expression for first law of

thermodynamics for a steady state flow process.

b) A particular substance undergoes a mechanically reversible process, expanding

from an initial state of 20 bar to final state of 8 bar. The path for the process is

described by the equation ( ) 4

036.0

−=

tV

P where P is in bar and Vt is in m3.

If tV∆ for the change of state is -1400J, determine W, a and tH∆ .

2. Air is compressed from an initial condition of 1 bar and 25oC to a final state of 5

bar and 25oC by three different mechanically reversible processes.

(a) Heating at constant volume followed by cooling at constant pressure.

(b) Isothermal compression.

( c) Adiabatic compression followed by cooling at constant volume. At these

conditions air may be considered as an ideal gas with the constant heat capacities

Cv =

2

5

R and CP =

2

7

R. Calculate the work required, heat transferred and

the changes in the internal energy and enthalpy of air for each process.

3. Calculate the molar volume of saturated liquid and the molar volume of saturated

vapor by the Redlich Kwong equation for the propose at 40o C where Psat = 13.7

bar.

Given that, TC = 369.8K, PC = 42.5 bar, W = 0.152, VC = 203 cm3/mol,

ZC = 0.281.

4.a) What are the different statements of second law of thermodynamics. Show that

the efficiency of an irreversible heat engine is always than of a reversible heat

engine.

b) One kilogram of water at the constant pressure of 1 atm, raised from 25oC to the

boiling point and then completely vapourized at this pressure. What is the

entropy change of the given process. Latent heat of vaporization at 1 atm is

2257 kJ/kg, CP = 4.184

kgK

kJ

Contd……2

Set No:

2

Page 5

Code No:220802

II.B.Tech II-Semester. Supplementary Examinations. January,2003

CHEMICAL ENGINEERING THERMODYNAMICS

(Chemical Engineering)

Time: 3 hours. Max.Marks:80

Answer any FIVE questions

All questions carry equal marks.

---

1.a) Distinguish between state function and path function.

b) Distinguish between a reversible process and an irreversible process.

c) A certain gas obeys the relation

+

2V

a

P (V-b) = RT where a,b and R are

constants. Derive a relation for the work done by the gas when it changes from

V1, T to V2, T.

2.a) State the first law of thermodynamics. Derive an expression for first law of

thermodynamics for a steady-state flow process.

b) For one mole of an ideal gas undergoing reversible adiabatic process, show that

PVr = constant. Where r = CP/Cv.

3.a) One kilo mole of methane is stored in a 0.3m3 tank at 300 0K. Estimate the

pressure of the gas using ideal gas law and Redlich-Kwong equation of state.

TC = 190.6 oK PC = 4.6 MPa

b) State Two parameter and three parameter law of corresponding states. Explain

Pitzer’s modification to law of corresponding states.

4.a) What do you mean by criterion of Exactness? Using criterion of Exactness derive

the four Maxwell relations.

b) Consider S=S(T,P) and S=S(T,V) and derive the following relations:

(i) T ds = Cp dT - ΤVβ dp

(ii) T ds = CV dT +

K

Tβ

dV

5.a) A Turbine in a steam power plant operating under steady state receives 1 kg/s

super heated steam at 3.0 MPa and 3000C. The steam enters the turbine with a

velocity of 10 m/s at an elevation of 5 m above the ground level. The Turbine

discharges wet steam 50 KPa pressure with a velocity of 50 m/s at an elevation of

10m above the ground level. The energy losses as heat from the Turbine casing

are estimated to be 10 KJ/s. Estimate the power output of the Turbine.

Enthalpy of super heated steam at 3 MPa and 300oC = 2993.5

kg

kJ

Enthalpy of wet steam at 50 kPa = 2300.08 kJ/kg.

Contd….2

Set No:

3

Page 6

Code No;220802 -2- Set No:3

b) An ideal gas (r=1.4) at 0.1 MPa and 300 oK enters an adiabatic compressor at the

rate of 1 mol/s and leves at 750 oK. Calculate the power consumed by the

compressor.

6.a) A reversible heat engine A absorbs energy from a reservoir at T1 and rejects energy

to a reservoir at T2. A second reversible engine B absorbs the same amount of

energy as rejected by the engine A from the reservoir at T2 and rejects energy to a

reservoir at T3. What is the relation between T1, T2 and T3 if:

(i) The efficiencies of engines A and B are same.

(ii) The work delivered by the engines are same

One mole of Nitrogen Cr=1.4) at 0.1 MPa and 300 oK. has been subjected to a

series of processes as a result of which it reached the state P=0.5 MPa and 600 0K

Determine the change in Entropy of Nitrogen. Nitrogen may be treated as an ideal

gas.

7.a) An insulated and rigid container is divided into two compartments. care

compartment contains 2 kmol Melium at 1.0 MPa and 600 0K, while the second

compartment contains 5 Kmol air at 2.0 MPa and 500 0K. The partition is

punctured and the gases are allowed to mix. Calculate the entropy change

associated with this process. Helium and air may be treated as ideal gases.

CV(He) = 1.5 R kJ/Kmol - 0K and CV(air) = 2.5 R kJ|kmol- 0K.

b) Explain phase rule with suitable examples.

8.a) Calculate the standard heat of the following reaction at 1000 0K.

2 SO2 (g) + O2 (g) → 2 SO3 (g)

Data: CP0 (SO2) = 47.38 x 10-3 + 6.66x10-6 T

CP0 (SO3) = 67.01 x 10-3 + 8.78x10-6 T

CP0 (O2) = 30.25 x 10-3 + 4.21x10-6 T

Where CPo denotes the molar heat capacity in the ideal gas state and is given in

kJ/mole - 0K.

Take ∆ H0f 298 = - 197.78 kJ.

b) Define:

(i) Standard heat of reaction

(ii) Standard heat of formation.

*********

Page 7

Code No:220802

II.B.Tech II-Semester. Supplementary Examinations. January,2003

CHEMICAL ENGINEERING THERMODYNAMICS

(Chemical Engineering)

Time: 3 hours. Max.Marks:80

Answer any FIVE questions

All questions carry equal marks.

--

1.a) Define the following terms:

(i) Enthalpy (ii) Internal energy (iii) Gibbs energy (iv) Helmholtz free energy

b) Explain phase rule. Give suitable examples.

c) Distinguish between state function and path function.

d) State Zero’th law of thermodynamics.

e) Distinguish between closed system and open system

2.a) Heat in the amount of 5 kJ is added to a system while its internal energy decreases

by 10 kJ. How much energy is transferred as work? For a process causing the

same change of state but for which work is zero how much heat is transferred?

b) What do you mean by an intensive property and extensive property.

c) State the first law of thermodynamics. Derive an expression for first law of

thermodynamics for a steady state flow process.

3. An ideal gas CP =

2

5R

and CV =

2

3R

is changed from P1 = 1 bar and V1 = 10 m3

to P2 = 10 bar and V2 = 1 m3 by the following mechanically reversible processes:

a) Isothermal compression

b) Adiabatic compression followed by cooling at constant pressure.

c) Adiabatic compression followed by cooling at constant volume

d) Heating at constant volume followed by cooling at constant pressure

calculate Q,W, HU ∆∆ , for each of these processes.

4.a) Show that the vander waals constants a and b are given by :

a =

CP

CTR

64

27 22

and b =

C

C

P

RT

8

b) What is a cubic equation of state ? Give few examples for cubic equations of state.

c) An empirical equation, PV = constant, where δ is a constant B sametimes used to

relate P and V for any mechanically reversible process. Assuming the validity of

this equation for an ideal gas, show that:

ω

=

1

1

−δ

RT

−

−

δ

δ 1

1

21

P

P

Contd……..2

Set No:

4

Code No:220802

II.B.Tech II-Semester. Supplementary Examinations. January,2003

CHEMICAL ENGINEERING THERMODYNAMICS

(Chemical Engineering)

Time: 3 hours. Max.Marks:80

Answer any FIVE questions

All questions carry equal marks.

---

1. Explain the following and give two examples of each

a) (i) Extensive and Intensive properties.

(ii) Reversible and irreversible processes.

(iii) State function and path function.

b) Water flows through a horizontal coil heated from the outside by high temperature

flue gases. As it passes through the coil, the water changes state from 2 atm

(202.66 KPa) and 180o F (82.2oC) to 1 atm (101.33 KPa) and 250o F (121.1oC).

Its entering velocity is 10 ft/sec (3.05 m/s) and its exit velocity is 600 ft/s

(182.9 m/s) Determine the heat transferred through the coil per unit mass of

water. Enthalpies of the inlet and outlet water streams are

inlet = 148 Btu/lbm (344.2 KJ/kg)

output = 1168.8 Btu/lbm (2718.5 KJ/kg)

2. a) Explain the application of cubic equations of state.

b) Determine the molar volume of n-butane at 510oK and 25 bar by each of the

following.

(i) The ideal gas equation

(ii) The generalized compressibility factor correlation

(iii) The generalized virial - coefficient correlation.

3. a) If 10 moles of ethylene is heated from 200oC to 1000oC in a steady flow process

at approximately atmospheric pressure. What is its entropy change. Give that,

A = 1.424; B = 14.394 x 10-3; C = -4.392 x 10-6; D = 0.

b) One mole of an ideal gas is compressed isothermally but irreversibly at 400 K

from 3 bar to 7 bar in a piston cylinder device. The work required is 35% greater

than the work of irreversible isothermal compression. The heat transferred from

the gas during compression flows to a heat reservoir at 300 K. Calculate the

entropy changes of gas, reservoir and ∆ S total.

4. a) For acetone at 20oC and 1 bar β = 1.487x10-3 / 0C , K = 62X10-6/bar,

V = 1.287

gm

cm3

Find (i) The value of

vT

P

∂

∂

(ii) The pressure generated when acetone is heated at constant volume from

20oC and 1 bar to 30oC.

(iii) The volume change when acetone is changed from 20oC and 1 bar to 0oC

and 10 bar

Contd…….2

Set No:

1

Page 2

Code No:220802 -2- Set No:1

b) Show that

(i)

+

∂

∂

=

∂

∂

pTH C

T

P

V

P

V

PP C

V

T

V

−

∂

∂ 2

PT

V

∂

∂

(ii) S

OTPT

PC

T

A

v

v

s

−

∂

=

∂

∂

/(

5. a) Derive Maxwell’s equations, explain their importance.

b) Estimate VR, HR and SR for steam at 200oC and 1400 kpa by using generalized

correlations. Given that TC = 647.3 K, PC = 220.5 bar, VC = 56 cm3/mol

W = 0.344.

6. Calculate Z and V for methanol vapour at 200oC and 10 bar by the following

equations.

a) A truncated virial equation

2

1

V

C

V

B

RT

PV

Z ++== with the following values of

virial coefficients, B = -219 cm3/mol, C = -17,300 cm6/mol.

b) The truncated virial equation

RT

BP

RT

PV

Z +== 1 with a value of B from the

generalized pidzer correlation.

c) The Red lich -Kwong equation with estimates of a and b given, Tc = 512.6K,

Pc = 81 bar W = 0.564.

7. a) Explain about the variations of heat capacity of a substance with temperature.

b) How much heat would be absorbed or released from hydrogenation of acetylene

to ethane at standard conditions.

C2 H2 (g) + 2H2 (g) C2 H6(g)

(i) Use heat of combustion data

(ii) Use heat of formation data.

Combustion data at 25oC : C2 H2 : ∆HoC = -310620 cal/gm

C2 H6 : ∆HoC = -372820 cal/gm

H2 : ∆HoC = -68317 cal/gm

Heat of formation data at 25oC:

C2 H2 : ∆Hƒ = 54194 cal/g.mole

C2 H6 : ∆Hƒ = -20236 cal/g.mole

8. Write short notes on any two of the following.

(i) Phase rule and criterion for equilibrium.

(ii) Heat effects of Industrial reactions.

(iii) Thermodynamic properties of an ideal bas.

@@@@@

Page 3

Code No:220802

II.B.Tech II-Semester. Supplementary Examinations. January,2003

CHEMICAL ENGINEERING THERMODYNAMICS

(Chemical Engineering)

Time: 3 hours. Max.Marks:80

Answer any FIVE questions

All questions carry equal marks.

---

1. a) State the first law of thermodynamics. Obtain an expression for first law of

thermodynamics for a steady state flow process.

b) A particular substance undergoes a mechanically reversible process, expanding

from an initial state of 20 bar to final state of 8 bar. The path for the process is

described by the equation ( ) 4

036.0

−=

tV

P where P is in bar and Vt is in m3.

If tV∆ for the change of state is -1400J, determine W, a and tH∆ .

2. Air is compressed from an initial condition of 1 bar and 25oC to a final state of 5

bar and 25oC by three different mechanically reversible processes.

(a) Heating at constant volume followed by cooling at constant pressure.

(b) Isothermal compression.

( c) Adiabatic compression followed by cooling at constant volume. At these

conditions air may be considered as an ideal gas with the constant heat capacities

Cv =

2

5

R and CP =

2

7

R. Calculate the work required, heat transferred and

the changes in the internal energy and enthalpy of air for each process.

3. Calculate the molar volume of saturated liquid and the molar volume of saturated

vapor by the Redlich Kwong equation for the propose at 40o C where Psat = 13.7

bar.

Given that, TC = 369.8K, PC = 42.5 bar, W = 0.152, VC = 203 cm3/mol,

ZC = 0.281.

4.a) What are the different statements of second law of thermodynamics. Show that

the efficiency of an irreversible heat engine is always than of a reversible heat

engine.

b) One kilogram of water at the constant pressure of 1 atm, raised from 25oC to the

boiling point and then completely vapourized at this pressure. What is the

entropy change of the given process. Latent heat of vaporization at 1 atm is

2257 kJ/kg, CP = 4.184

kgK

kJ

Contd……2

Set No:

2

Page 5

Code No:220802

II.B.Tech II-Semester. Supplementary Examinations. January,2003

CHEMICAL ENGINEERING THERMODYNAMICS

(Chemical Engineering)

Time: 3 hours. Max.Marks:80

Answer any FIVE questions

All questions carry equal marks.

---

1.a) Distinguish between state function and path function.

b) Distinguish between a reversible process and an irreversible process.

c) A certain gas obeys the relation

+

2V

a

P (V-b) = RT where a,b and R are

constants. Derive a relation for the work done by the gas when it changes from

V1, T to V2, T.

2.a) State the first law of thermodynamics. Derive an expression for first law of

thermodynamics for a steady-state flow process.

b) For one mole of an ideal gas undergoing reversible adiabatic process, show that

PVr = constant. Where r = CP/Cv.

3.a) One kilo mole of methane is stored in a 0.3m3 tank at 300 0K. Estimate the

pressure of the gas using ideal gas law and Redlich-Kwong equation of state.

TC = 190.6 oK PC = 4.6 MPa

b) State Two parameter and three parameter law of corresponding states. Explain

Pitzer’s modification to law of corresponding states.

4.a) What do you mean by criterion of Exactness? Using criterion of Exactness derive

the four Maxwell relations.

b) Consider S=S(T,P) and S=S(T,V) and derive the following relations:

(i) T ds = Cp dT - ΤVβ dp

(ii) T ds = CV dT +

K

Tβ

dV

5.a) A Turbine in a steam power plant operating under steady state receives 1 kg/s

super heated steam at 3.0 MPa and 3000C. The steam enters the turbine with a

velocity of 10 m/s at an elevation of 5 m above the ground level. The Turbine

discharges wet steam 50 KPa pressure with a velocity of 50 m/s at an elevation of

10m above the ground level. The energy losses as heat from the Turbine casing

are estimated to be 10 KJ/s. Estimate the power output of the Turbine.

Enthalpy of super heated steam at 3 MPa and 300oC = 2993.5

kg

kJ

Enthalpy of wet steam at 50 kPa = 2300.08 kJ/kg.

Contd….2

Set No:

3

Page 6

Code No;220802 -2- Set No:3

b) An ideal gas (r=1.4) at 0.1 MPa and 300 oK enters an adiabatic compressor at the

rate of 1 mol/s and leves at 750 oK. Calculate the power consumed by the

compressor.

6.a) A reversible heat engine A absorbs energy from a reservoir at T1 and rejects energy

to a reservoir at T2. A second reversible engine B absorbs the same amount of

energy as rejected by the engine A from the reservoir at T2 and rejects energy to a

reservoir at T3. What is the relation between T1, T2 and T3 if:

(i) The efficiencies of engines A and B are same.

(ii) The work delivered by the engines are same

One mole of Nitrogen Cr=1.4) at 0.1 MPa and 300 oK. has been subjected to a

series of processes as a result of which it reached the state P=0.5 MPa and 600 0K

Determine the change in Entropy of Nitrogen. Nitrogen may be treated as an ideal

gas.

7.a) An insulated and rigid container is divided into two compartments. care

compartment contains 2 kmol Melium at 1.0 MPa and 600 0K, while the second

compartment contains 5 Kmol air at 2.0 MPa and 500 0K. The partition is

punctured and the gases are allowed to mix. Calculate the entropy change

associated with this process. Helium and air may be treated as ideal gases.

CV(He) = 1.5 R kJ/Kmol - 0K and CV(air) = 2.5 R kJ|kmol- 0K.

b) Explain phase rule with suitable examples.

8.a) Calculate the standard heat of the following reaction at 1000 0K.

2 SO2 (g) + O2 (g) → 2 SO3 (g)

Data: CP0 (SO2) = 47.38 x 10-3 + 6.66x10-6 T

CP0 (SO3) = 67.01 x 10-3 + 8.78x10-6 T

CP0 (O2) = 30.25 x 10-3 + 4.21x10-6 T

Where CPo denotes the molar heat capacity in the ideal gas state and is given in

kJ/mole - 0K.

Take ∆ H0f 298 = - 197.78 kJ.

b) Define:

(i) Standard heat of reaction

(ii) Standard heat of formation.

*********

Page 7

Code No:220802

II.B.Tech II-Semester. Supplementary Examinations. January,2003

CHEMICAL ENGINEERING THERMODYNAMICS

(Chemical Engineering)

Time: 3 hours. Max.Marks:80

Answer any FIVE questions

All questions carry equal marks.

--

1.a) Define the following terms:

(i) Enthalpy (ii) Internal energy (iii) Gibbs energy (iv) Helmholtz free energy

b) Explain phase rule. Give suitable examples.

c) Distinguish between state function and path function.

d) State Zero’th law of thermodynamics.

e) Distinguish between closed system and open system

2.a) Heat in the amount of 5 kJ is added to a system while its internal energy decreases

by 10 kJ. How much energy is transferred as work? For a process causing the

same change of state but for which work is zero how much heat is transferred?

b) What do you mean by an intensive property and extensive property.

c) State the first law of thermodynamics. Derive an expression for first law of

thermodynamics for a steady state flow process.

3. An ideal gas CP =

2

5R

and CV =

2

3R

is changed from P1 = 1 bar and V1 = 10 m3

to P2 = 10 bar and V2 = 1 m3 by the following mechanically reversible processes:

a) Isothermal compression

b) Adiabatic compression followed by cooling at constant pressure.

c) Adiabatic compression followed by cooling at constant volume

d) Heating at constant volume followed by cooling at constant pressure

calculate Q,W, HU ∆∆ , for each of these processes.

4.a) Show that the vander waals constants a and b are given by :

a =

CP

CTR

64

27 22

and b =

C

C

P

RT

8

b) What is a cubic equation of state ? Give few examples for cubic equations of state.

c) An empirical equation, PV = constant, where δ is a constant B sametimes used to

relate P and V for any mechanically reversible process. Assuming the validity of

this equation for an ideal gas, show that:

ω

=

1

1

−δ

RT

−

−

δ

δ 1

1

21

P

P

Contd……..2

Set No:

4