CHE2164
MEC2405
JUN 2007
Office Use Only
Monash University
Semester One Examination Period
2007
Faculty Of Engineering
EXAM CODES:
CHE2164 / MEC2405
TITLE OF PAPER:
THERMODYNAMICS I - PAPER 1
EXAM DURATION:
3 hours writing time
READING TIME:
10 minutes
THIS PAPER IS FOR STUDENTS STUDYING AT:( tick where applicable)
 Berwick
 Clayton
 Malaysia
 Off Campus Learning
 Caulfield
 Gippsland
 Peninsula
 Enhancement Studies
 Pharmacy
 Other (specify)
 Open Learning
 Sth Africa
During an exam, you must not have in your possession, a book, notes, paper, calculator, pencil case, mobile
phone or other material/item which has not been authorised for the exam or specifically permitted as noted
below. Any material or item on your desk, chair or person will be deemed to be in your possession. You are
reminded that possession of unauthorised materials in an exam is a discipline offence under Monash Statute
4.1.
AUTHORISED MATERIALS
CALCULATORS
 YES
 NO
OPEN BOOK
 YES
 NO
SPECIFICALLY PERMITTED ITEMS
if yes, items permitted are:
 YES
 NO
Candidates must complete this section if required to write answers within this paper
STUDENT ID
__ __ __ __ __ __ __ __
DESK NUMBER
__ __ __ __
Page 1 of 11
CHE2164
MEC2405
JUN 2007
ANWERING INSTRUCTIONS FOR CANDIDATES
1. ATTEMPT ALL QUESTIONS (6)
2. MARKS FOR EACH QUESTION ARE INDICATED. THE INDICATED MARKS SUM TO
100
3. SELECTED FORMULAE ARE ATTACHED AS PAGE 10
4. A T-s DIAGRAM FOR STEAM IS INCLUDED AS AN ACCOMPANYING CHART AND
MUST BE RETURNED
5. A P-h DIAGRAM FOR R134a IS INCLUDED AS AN ACCOMPANYING CHART AND
MUST BE RETURNED
6. A SET OF THERMODYNAMIC PROPERTY TABLES FOR R134a IS INCLUDED AS AN
ACCOMPANYING SET OF TABLES
7. THE DATA BELOW SHOULD BE USED WHEREVER RELEVANT
R = 8.314 J.mol-1.K-1
Molecular weight of Air = 29.0 kg/kmol
Page 2 of 11
CHE2164
MEC2405
JUN 2007
Question 1 [15 Marks]
An insulated piston-cylinder device contains R134a initially at 1000 kPa and 50°C. Two
different processes are carried out, each starting from the same initial state.
(a) Process 1: The piston is allowed to expand reversibly until the pressure has reached 60 kPa.
Determine the final temperature (K), the change in internal energy (kJ/kg) of the R134a, the
work done (kJ/kg) (using the sign convention), and the change in entropy (kJ/kg.K) of the
R134a.
(b) Process 2: The piston is allowed to expand irreversibly until the pressure is once again 60
kPa and the work is measured and found to be 40.34 kJ/kg. Determine the final temperature
(K), the entropy generated (kJ/kg.K) and the isentropic efficiency of the process.
Page 3 of 11
CHE2164
MEC2405
JUN 2007
Question 2 [20 Marks]
Consider a steam power plant operating on the ideal Rankine cycle with inter-stage reheat. There
are two turbine stages. The steam enters the first turbine stage at 30 MPa and 500°C and leaves
at 80 bar to be reheated to 500°C The condenser operates at a pressure of 60 kPa. The turbine
has an isentropic efficiency of 67% (both stages) and there is no pressure drop in the boiler,
condenser and inter-stage reheater. Steam leaves the condenser and enters the pump as saturated
liquid at the condenser pressure. Ignore pump work. The flow rate of the steam/water is 1565
kg/hr.
a)
b)
c)
d)
e)
Sketch the equipment diagram of the power plant showing the condenser, boiler, turbine
(both stages and reheater) and pump. Number each stream clearly and show the flow
direction. Identify Wnet,out, QH and QL.
Sketch the cycle on the T-s diagram for steam clearly showing the corresponding labels and
flow direction. Also identify the points at the exit of each turbine stage which correspond to
completely (100%) isentropic expansion. Use calculations to explain how you identified the
locations of the two points corresponding to the exit of each turbine stage.
Determine the duty (kW) in the boiler, condenser, and reheater.
Determine the power output from both stages of the turbine (kW).
Determine the thermal efficiency of the cycle.
Page 4 of 11
CHE2164
MEC2405
JUN 2007
Question 3 [15 Marks]
Consider the Brayton Cycle for gas-turbine heat engines as shown below. Air is compressed
from P1=250kPa, T1=25°C to P2=1300 kPa. The inlet temperature to the turbine is
T3=1000°C. The compressor and turbine are both adiabatic and both have isentropic
efficiencies of 75%.
Use air-standard assumptions, Cp=1.005 kJ/kg.K (constant), k=1.4 (constant)
Calculate:
a. The temperature (K) at the compressor exit (T2)
b. The specific compressor work (kJ/kg)
c. The temperature (K) at the turbine exit (T4)
d. The specific turbine work (kJ/kg)
e. The net work (kJ/kg) and the back work ratio
f. Specific heat transfers q̂ in and q̂ out (kJ/kg)
g. The thermal efficiency
h. The mass flow rate (kg/s) to produce 3 MW of net power
Page 5 of 11
CHE2164
MEC2405
JUN 2007
Question 4 [15 Marks]
A refrigerator uses R-134a as the working fluid and operates on an ideal vapour-compression
cycle between 0.2 and 1.0 MPa. The mass flow rate of the refrigerant is 0.1 kg/s. There is 10°C
of superheating in the evaporator and no sub-cooling in the condenser. There is no pressure
drop in the evaporator or condenser. The compressor has an isentropic efficiency of 100%. The
expansion valve is well insulated.
a. Sketch the cycle showing the condenser, evaporator, compressor and expansion valve and
indicate the flow direction. Label each stream carefully. Sketch the cycle on the P-h
diagram for R-134a provided. Clearly show the corresponding labels on your P-h diagram.
b. Determine the quality of the R-134a leaving the expansion valve.
c. Calculate the rate of entropy generated across the expansion valve (kJ/K.s).
d. Calculate the rate of heat removal (kW) from the refrigerated space and the power (kW)
input to the compressor.
e. Calculate the rate of heat rejection to the environment (kW)
f. Calculate the COP of the refrigerator.
Page 6 of 11
CHE2164
MEC2405
JUN 2007
Question 5 [15 Marks]
Part (A) – 5 marks
Answer the following questions and/or tasks, in each case carefully explaining your answer:
1. In the ideal Rankine cycle, all steps are reversible. Explain why the thermal efficiency of
the ideal Rankine cycle is lower than the efficiency of a Carnot cycle operating between the
same high and low temperatures.
2. The entropy of a hot baked potato decreases as it cools. Is this a violation of the Second
Law of Thermodynamics?
3. Are the efficiencies of all work producing devices limited by the Second Law of
Thermodynamics? Give examples to illustrate your answer.
4. A system undergoes a process between two fixed states, first in a reversible manner and then
in an irreversible manner. For which case is the entropy change greater?
5. Explain why heat transfer across a finite temperature difference is an irreversible process.
Part (B) – 10 marks
An ideal gas is to be compressed from 1bar, 20°C to 10 bar. If the gas flow rate is 1000 kg/hr,
calculate the compressor power (kW) for the following cases:
a) single stage, isentropic compression
b) single stage, isothermal compression
c) ideal two stage isentropic compression
Data for the ideal gas: Cp=1.005 kJ/kg.K (constant), k=1.4 (constant), M=29kg/kmole
Page 7 of 11
CHE2164
MEC2405
JUN 2007
Question 6 [20 marks]
Part (A) - 4 marks
A flat plate collector has conversion efficiency of 45% and an area of 2.1 m2. For a monthly
average daily global radiation on a horizontal surface of 9 MJ/m2, find:
(i)
the useful heat that can be produced when the collector is inclined at 38 with the
horizontal
(ii)
the volume of water (in litres) that can be heated daily by this system from 20 to 70C.
Take the density of water as 989 kg/m3 and specific heat as 4180 J/kg.K
Part (B) – 6 marks
The figures below show the wind speed distribution at a certain site and the power curve of a
wind turbine. Estimate the annual total wind energy output at this site and the revenue per year
if electric power produced is sold to the utility at $0.06/kWh.
600
700
800
250
200
400
500
600
400
800
980
1050
1000
960
800
1000
350
100
200
30
20
10
5
5
0
0
0
0
0
0
0
Hours per year of each bin
1200
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Wind speed (m/s)
350
Power output (kW
300
288
250
200
150
100
50
Power = 18x(wind speed - 4)2 for
wind speed between 4 and 8 m/s
0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
Wind speed (m/s)
Page 8 of 11
CHE2164
MEC2405
JUN 2007
Part (C) - 6 marks
List the benefits and drawbacks of hydroelectric power.
A reservoir with surface area of 1.5 km2 and mean depth of 6.0 m is built at 300 m elevation
above sea level part way down a mountain. The reservoir water may be discharged through the
turbines in a hydroelectric power plant and then into a river both located at 150 m elevation
above sea level. Assuming no friction losses in the penstock and conversion efficiency is 85%,
estimate the amount of electric energy (in kWh) that can be generated by the power plant. Take
the density of water as 1000 kg/m3.
Part (D) - 4 marks
Discuss briefly ANY TWO (2) of the following methods employed in biomass energy
extraction:
(i)
direct combustion
(ii)
gasification
(iii)
pyrolysis
(iv)
anaerobic digestion
Page 9 of 11
CHE2164
MEC2405
JUN 2007
FORMULAS -THERMODYNAMICS I
1. PROPERTIES OF PURE SUBSTANCES
ˆ U
ˆ  PV
ˆ  
H

Û  xÛ g  (1 - x)Û f 
V̂  xV̂g  (1 - x)V̂f 
R
Ru

M


x
m total
PV̂  RT 
Ŝ  xŜ g  (1 - x)Ŝ f 

m vapor
U  mÛ; H  mĤ; S  mŜ; V  mV̂
2. ENERGY ANALYSIS OF CLOSED SYSTEMS
2.1 General Balance
Ê sys  Û sys  KE sys  PE sys 
Ê sys  Q̂ - Ŵb 
mQ̂  Q, mŴb  Wb 
2.2 Boundary Work
 V̂ 
Ŵb,isothermal  RTln 2  
 V̂1 
Ŵb   Pd V̂ 
Ŵb, polytropic 
(P2 V̂2  P1V̂1 ) 
1 n
(P2 V̂2  P1V̂1 ) 
1 k

2.3 Changes in Internal Energy and Enthalpy

Û   Ĉ v dT  Ĉ v,avg T2  T1  
k

Ŵb, isentropic 
Ĉ p
Ĉ v
Ĥ   Ĉ p dT  Ĉ p, avg T2  T1  


Ĉ p  Ĉ v  R (ideal gas)

3. ENERGY ANALYSIS OF OPEN SYSTEMS AND SHAFT WORK
3.1 General Unsteady Balance

 


V2
V2
 W
  m
  m





Ĥ
gz
Q
W
Ĥ



 gz 
E sys  Q


in
in
out
out



2
2
in
out




3.2 Steady State, no boundary work


 

V2
V2
 W


  Ĥ 
  Ĥ 
Q
 gz 
 gz   Q
in
sh,in   m
out  Wsh,out   m
2
2
in
out




3.3 Steady State, single inlet and exit, no boundary work, ignore changes in KE,PE

 m
 Q̂ in  Ŵsh,in - Q̂ out - Ŵsh,out
H

3.4 Shaft Work - general
Ŵsh    V̂ dP
3.5 Shaft Work – isentropic compression/expansion
 P  ( k 1) / k 
k (P2 V̂2 - P1V̂1 )
RT
k
1
or Ŵsh 
Ŵsh 
 2 
 1
1- k
1 - k  P1 


3.5 Shaft Work – isothermal compression/expansion
P 
Ŵsh  RTln 2 
 P1 
3.6 Shaft Work – ideal 2-stage compression – interstage pressure Px
Px  P1 P2 ; Ŵsh,stage1  Ŵsh,stage2
Page 10 of 11
CHE2164
MEC2405
JUN 2007
4. SECOND LAW OF THERMODYNAMICS AND ENTROPY
4.1 Heat Engines
 th 
Wnet,out
QH
 th,Carnot  1
,
 QL 
T

  L
 Q H  rev TH
TL
,
TH
4.2 Heat Pumps and Refrigerators
COPREF 
QL
Win
COPHP 
4.3 Entropy
δQ
 T 0
QH
Win
COPHP  COPREF  1
2
 δQ 
S  S2  S1   

T int,rev
1
2
 δQ 
Ssys  S2  S1      Sgen
T 
1
dS 
Q
T
STOT  SSYS  SSURR  Sgen  0
4.4 Isentropic Processes
T2  P2 
 
T1  P1 
ˆ k  constant
PV
( k 1) / k
T2  V1 

T1  V2 
( k 1)
P2  V1 
 
P1  V2 

k
4.5 General Processes
TdŜ  dÛ  PdV̂
TdŜ  dĤ  V̂dP
4.5.1 Entropy change of liquids and solids
2
S2  S1   C(T)
1
T 
dT
 Cavg ln 2 
T
 T1 
4.5.1 Entropy change of ideal gases
T
S  C p,avg ln  2
 T1
4.6 Isentropic Efficiencies
W
 turb  act
Wisen
4.7 Entropy Balance
 comp 
P

  R ln  2

 P1

T
  C v,avg ln  2

 T1

V
  R ln  2

 V1



Wisen
Wact
S sys  
Qk
  miŜi   miŜi  S gen
Tk
in
out
5. POWER CYCLES

 th, Brayton  1 
1
( k 1) / k
p
r
, rp 
P2
  th,Otto  1  ( k11) , r  V̂max 
P1
r
V̂min

6. RENEWABLE ENERGY
6.1 Solar Power

Q th

GTA
GT  G H
cos( )  
cos(   )
  ab
T

fi
 T 
GT
6.1 Wind Power
E  2.4R 2 c 3 
1
P  R 2 c 3 
2
Page 11 of 11