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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]