King Fahd University of Petroleum and Minerals
Mechanical Engineering Department
Thermodynamics II (ME204)
Final Exam (Term 011)
13-10-2001
9th Jan., 2002
Duration: 2 hours 30 minutes
Student Name:
ID #
:
Serial #
:
Dr. M. A. Antar
Closed Book/Closed Notes Exam
A Formula sheet is provided
Problem
Mark
1
2
3
4
Total grade
25
25
25
25
100
This exam contains 9 pages including the cover page.
Note, for SSSF process

 
 
 

v2
v2
Q  m i  hi  i  gz i   W   m e  he  e  gz e 
2
2




For Ideal Gas
T
P
s 2  s1  c P ln 2  R ln 2
T1
P1
Grade
Earned
Problem # 1
In a particular reheat-cycle power plant, steam enters the high-pressure
turbine at 5 MPa, 450C and expands to 0.5 MPa, after which it is reheated to
450C. The steam is then expanded through the low-pressure turbine to 7.5
kPa. Liquid water leaves the condenser at 30C, is pumped to 5 MPa, and
then returned to the steam generator. Each turbine is adiabatic with an
isentropic efficiency of 87% and the pump efficiency is 82%. If the total power
output of the turbines is 10 MW.
a. Sketch the T-s diagram & Determine the mass flow rate of steam
b. Determine the pump power input
c. Determine the thermal efficiency of the power plant.
d. If the ambient condition is 25 oC and 0.1 MPa, determine the
availability of the turbine.
Problem # 2
A flow moist air at 100 kPa, 40C, 40% relative humidity is cooled to 15C
(where 2 = 100 %) in a
constant pressure SSSF device.
a. Find the humidity ratio of the inlet flow.
b. Find the humidity ratio of the exit flow.
c. Find the heat transfer in the device per kg dry air.
Problem # 3
Develop an expression for the variation in temperature with pressure in a
constant entropy process, ( T/ P)s , that only includes the properties P–v–T
and the specific heat, Cp .
An uninsulated compressor delivers ethylene, C2 H4 , to a pipe, D 10 cm, at
10.24 MPa, 94C and velocity 30 m/s. The ethylene enters the compressor at
6.4 MPa, 20.5C and the work input required is 300 kJ/kg. Find
a. Ze and specific volume ve.
b. The mass flow rate,
c. The total heat transfer
d. Entropy generation, assuming the surroundings are at 25C.
Additional sheet for Problem # 3
Problem # 4
In a new high-efficiency furnace, natural gas, assumed to be 90% methane
and 10% ethane (by volume) each enter at 25C, 100 kPa, and the products
(assumed to be 100% gaseous) exit the furnace at 77C, 100 kPa.
a. Write the Stoichiometric combustion equation.
b. Write the combustion equation for 110 % theoretical air.
c. Consider 110 % theoretical air case, what is the heat transfer for this
process?
d. Compare the heat transfer rate to that of an older furnace where the
products exit at 227oC, 100 kPa.
Formula Sheet
Chapter 10:
rev
Q0 = T o ( S2  S1 )1 Q2
Reversible heat transfer for a control mass:
T0
TH
W 2 = 1 Q2  Q0rev  (U 2  U 1 )  T o ( S 2  S1 )  (U 2  U 1 ) 1 Q2 (1 
rev
Reversible work for a control mass:
1
Irreversibility for a control mass:
1
I 2 = 1W 2rev  1W 2ac = T o ( S 2  S1 ) 
 dS c.v.
Reversible heat transfer for an SSSF process: Q c.v.,0 = T o 
 dt
rev
T0
1 Q2
]  T0 S net
1 Q 2  T0 [( S 2  S 1 ) 
TH
TH

T
+  m e s e -  m i s i  -  o Q c.v, H
TH


 i htot,i - T 0 si  -  m e htot,e - T 0 s e +  1 Reversible work for an SSSF process: W c.v.=  m
rev

where htot  h +
T 0  
 Q c.v.H
TH 
1 2
V + gZ
2
ac
rev
ac

Irreversibility for an SSSF process: Ic.v.= W c.v. - W c.v.= Q
- Qc.v.,0
 T 0 S gen,c.v.
c.v.,0
rev


1 2

V + gZ  - ho - T 0 s0 + gZ 0 
2


T 0  
ac
Ic.v.=   m i  i -  m e  e  +   1  Q c.v.,H - W c.v.
TH 

Flow availability:  =  h - T 0 s +
Non-flow availability:  = e - T 0 s  - eo - T o so  + Po v - vo   e + P0 v - T o s  - e0 + P0 v0 - T 0 s0 
e  u + V2/2 + gZ
where

T o 
ac
I 2 = m  1 -  2  +   1  .1 Q 2,c.v.,H - .1 W 2 - P0 ( V 2 - V 1 )
TH 

1

Second-law efficiency:  2nd
wa
for turbine;
law =
i -e
P-v relations for ideal gas (with constant Cp):
 2nd law =
and
n
1 1
Chapter 12:
Mass fraction: ci =
Mole fraction: yi =
y Mi
/n
mi
n
n
= i M i = i M i tot = i
mtot  ni M j  ni M j / ntot  y j M j
ni
mi / M i
mi / ( M i mtot )
c /
=
=
= i Mi
ntot  m j / M j  m j / ( M j mtot )  c j / M j
Relative humidity:  =
Pv =  v = v g
P g  g vv
Humidity ratio:  = 0.622
=
Pv
Pa
 Pa
0.622 P g
m A  A

n
2
for heat exchangers.
m B  B
T 2  p2 
Pv = constant = P v = P2 v  =  
T 1  p1 
n
T0
)
TH
n 1 / n
v 
=  1 
 v2 
n -1
Chapter 13:
 x   y 
   = 1
 y  z  x  z
Mathematical relations: 
 T 
 P 
= -   ,
 v s
 s v
Maxwell relations: 
 x   y   z 
      = - 1
 y  z  z  x  x  y
and
 T   v 

 =  ,
 P s  s  p
s g - s f s fg h fg
 dP 
=
=
 =
 dT sat v g - v f v fg Tv fg

Clapeyron equation: 
Reduced temperature, pressure and volume: P r =
 P   s 

 =  ,
 T v  v T
P
Pc
, Tr=
ln
T
Tc
P2 h fg  (T2  T1 ) 



P1
R  (T1  T2 ) 
, vr =
v
v 

dh  C p dT  v  T ( ) P  dP
T 

The change in internal energy:
 P

du  C v dT  T ( ) v  P  dv

T


The change in entropy:
ds  C v
dT
P
 ( ) v dv
T
T
and
*
*
*
*
h1 - h2 = - h1 - h1+ h1 - h2 + h2 - h2 
*
*
*
*
s1 - s 2 = - s1 - s1+ s1 - s 2  + s 2 - s 2 
Chapter 14:
Fuel-air ratio:
AF mass =
mair
m fuel
and
AF mole =
nair
n fuel
Equivalence ratio:  = FA / FAs = AFs / AF
h RP = H P - H R
Enthalpy of combustion:




o
o
h RP =  ne h f +  h e -  ni h f +  h i
P
R
P.v = ZRT
vc
The change in enthalpy:
Equations for generalized tables:
 v 
 s 

 = -
 .
 T  P
  P T
ds  C P
dT
v
 ( ) P dP
T
T