Total No. of Questions—12] [Total No. of Printed Pages—8+2

Seat

No. [4262]-189

S.E. (Chemical) (Second Semester) EXAMINATION, 2012

CHEMICAL ENGINEERING THERMODYNAMICS–I

(2008 PATTERN)

Time : Three Hours Maximum Marks : 100

N.B. :— (i) Answer three questions from Section I and three questions

from Section II.

(ii) Answers to the two Sections should be written in separate

answer-books.

(iii) Neat diagrams must be drawn wherever necessary.

(iv) Figures to the right indicate full marks.

(v) Use of logarithmic tables, slide rule, Mollier charts,

electronic pocket calculator and steam tables is allowed.

(vi) Assume suitable data, if necessary.

SECTION I

1. (a) One mole of an ideal gas is compressed in a piston cylinder

assembly from the initial state of 0.1 MPa and 300 K till its

volume is reduced to 1/15 of the original volume. The process

P.T.O.

[4262]-189 2

of compression can be approximated as a polytropic process

with n = 1.2. Determine the final temperature and pressure

of the gas. Also calculate the work done on the gas and the

heat interaction. [8]

(b) Water at 366.65 K is pumped from a storage tank at the rate

of 3.15 × 10–3 m3/s. The motor for the pump supplies work

at the rate of 1.5 kW. The water goes through a heat

exchanger giving up heat at the rate of 700 kW and is delivered

to a second storage at an elevation 15 m above the first tank.

Calculate the enthalpy of the water delivered to the second

tank ? Enthalpy at 366.65 K is 391.6 kJ/kg. [10]

Or

2. (a) Nitrogen gas is confined in a cylinder and the pressure of the

gas is maintained by a weight on the piston. The mass of the

piston and the weight together is 50 kg. The acceleration due

to gravity is 9.81 m/s2 and the atmospheric pressure is 1.01325

bar. Assume frictionless piston. Determine :

(i) The force exerted by atmosphere, the piston and the weight

on the gas if piston is 100 mm in diameter.

(ii) The pressure of the gas. [9]

[4262]-189 3 P.T.O.

(b) Explain phase rule. How many degrees of freedom has each

of the following systems ?

(i) Liquid water in equilibrium with its vapor.

(ii) Liquid water in equilibrium with a mixture of water vapor

and nitrogen.

(iii) A liquid solution of alcohol in water in equilibrium with

its vapor. [9]

3. (a) One mole of a gas which obeys the relation PV = RT is initially

at 300 K and 0.1 MPa. The gas is heated at constant volume

till the pressure rises to 0.5 MPa and then allowed to expand

at constant temperature till the pressure reduces to 0.1 MPa.

Finally the gas is returned to its original state by compressing

at constant pressure. Calculate the work done by the gas in

each of the processes and also estimate the net work done

by the gas. R = 8.314 J/mol.K. [10]

(b) A particular gas obeys the relation

2

P + (V ) RTV

ab

− =

where a, b, c are constants. Suppose the gas is allowed to

expand reversibly and at constant temperature from V1 to V2,

calculate the work done by the gas. [6]

[4262]-189 4

Or

4. An ideal gas initially at 600 K and 10 bar undergoes a four step

mechanically reversible cycle in a closed system. In step 1-2, pressure

decreases isothermally to 3 bar, in step 2-3, pressure decreases at

constant volume to 2 bar, in step 3-4, volume decreases at constant

pressure and in step 4-1, the gas returns adiabatically to its initial

state. Calculate Q, W, ∆E and ∆H for each step of cycle. Take

Cp = 7

2 R and Cv =

5

2 R. [16]

5. It is desired to carry out the following reaction at 800°C. Estimate

the standard enthalpy change of the reaction at 800°C if the standard

enthalpy change at 298 K is – 41.116 kJ [16]

CO + H2O → CO2 + H2

Cp° = a + bT + cT2 + dT3 + eT–2 J/mol°K T is in K.

The constants in the heat capacity equation are as follows :

Compound a b × 103 c × 106 d × 109 e × 10–5

CO 28.068 4.631 — — –0.258

H2O 28.850 12.055 — — 1.006

CO2 45.369 8.688 — — –9.619

H2 27.012 3.509 — — 0.690

[4262]-189 5 P.T.O.

Or

6. (a) Ethylene gas and steam at 593 K and atm. pressure are fed

to a reaction process in an equimolar mixture :

C2H4(g) + H2O(g) → C2H5OH(l)

Liquid ethanol exits the process at 298 K. What is the heat

transfer associated with this overall process per mole of ethanol

produced ? Use the following data : [10]

∆∆∆∆∆Hf298 J/mol A B×103 C×106 D×10–5

C2H4(g) 52510 1.424 14.394 –4.392 —

H2O(g) –241818 3.470 1.45 — 0.121

C2H5OH(l) –277690 3.518 20.00 –6.002 —

(b) Calculate the std. enthalpy change at 298.15 K for the

reaction : [6]

4 10 2 2 213

C H (g) + O (g) 4CO (g) + 5H O(g)2

→

from the following standard enthalpies of formation at

298 K :

Compound C4H10(g) CO2(g) H2O(g)

∆H°f298 (kJ) –74.943 –393.978 –241.997

[4262]-189 6

SECTION II

7. (a) A reversible heat engine operates with four thermal reservoirs.

Determine the heat interactions Q2 and Q4 : [8]

Thermal

reservior

800 k

Thermal

reservior

1000 k

Heat

Engine

Thermal

reservior

300 k

Thermal

reservior

500 k

W = 800 kJ

750 kJ

Q4Q3

Q1 Q2

1500 kJ

(b) A rigid vessel of 0.06 m3 volume contains an ideal gas

Cv = (5/2) R at 500 K and 1 bar.

(i) If heat in the amount of 15 kJ is transferred to the gas,

determine its entropy change.

(ii) If the vessel is fitted with stirrer that is rotated by a

shaft so that work in the amount of 15 kJ is done on

K Kreservoir reservoir

K

reservoir

K

reservoir

[4262]-189 7 P.T.O.

the gas, what is the entropy change of the gas if the

process is adiabatic ? What is ∆Stotal ? What is the

irreversible feature of the process ? [10]

Or

8. (a) A certain mass of air initially at 480 kPa and temperature

of 190°C is expanded adiabatically to 94 kPa. It is then heated

at constant volume until it attains its initial temperature when

the pressure is found to be 150 kPa. State the type of

compression necessary to bring back the system to its original

pressure and volume. Determine :

(i) Adiabatic expansion index

(ii) Work done per kg of air.

(iii) Change in entropy for all the steps. [12]

(b) Write a note on thermodynamic temperature scale. [6]

9. (a) Explain residual properties. Derive the following fundamental

residual property relation for 1 mol of a substance for closed

thermodynamic system : [8]

RR R

2

G P T= V – H .

RT T RT

d d d

d

[4262]-189 8

(b) State the defining equations for E, H, G and A. Using

principles of 1st and 2nd law of thermodynamics derive the

following property relations :

(i) dE = TdS – PdV

(ii) dH = TdS + Vdp

(iii) dG = VdP – SdT

(iv) dA = –PdV – SdT. [8]

Or

10. (a) The equation of state of a certain substance is given by the

expression :

3

RT CV

P T= −

and the specific heat is given by Cp = A + BT, where A,

B and C are constants. Derive the expressions for changes in

internal energy, enthalpy and entropy for :

(i) An isothermal process

(ii) An isobaric process. [10]

(b) Explain the terms volume expansivity, isothermal compressibility

and adiabatic compressibility. [6]

[4262]-189 9 P.T.O.

11. (a) Linde process is used for air liquefaction. The high pressure

gas leaving the compressor is at 120 bar and is cooled to

306 K (516 kJ/kg) before it is sent through the heat exchanger

where it exchanges heat with low pressure gas leaving the

separator at 2 bar. A 14 K approach is desired at the hot

end of the exchanger so that the low pressure gas leaving the

exchanger is at 292 K (526 kJ/kg). Enthalpy of saturated liquid

and saturated vapor at 2 bar are 121 kJ/kg and 314 kJ/kg

respectively. Determine :

(i) The fraction of the air liquefied during expansion.

(ii) Temperature of the air on the high pressure side of the

throttle valve. [10]

(b) What are the properties of refrigerant which are required

to be considered during choice of it for certain

application ? [6]

Or

12. (a) Explain air refrigeration cycle. [8]

(b) A house has a winter heating requirement of 30 kJ/s and a

summer cooling requirement of 60 kJ/s. Consider a heat pump

[4262]-189 10

installation to maintain the house temperature at 20°C in winter

and 25°C in summer. This requires circulation of the refrigerant

through exterior exchanger coils at 30°C in winter and 5°C in

summer. Underground coils provide the heat source in winter

and the heat sink in summer. For a year round ground

temperature of 15°C the heat transfer characteristics of the

coils necessitate refrigerant temperature of 10°C in winter and

25°C in summer. What are the minimum power requirements

for winter heating and summer cooling ? [8]