THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MECHANICAL AND MANUFACTURING ENGINEERING
JUNE 2007
MMAN2700 - THERMODYNAMICS
MECH2711 - THERMODYNAMICS A
MECH2712 - THERMODYNAMICS B
1.
Time allowed - THREE (3) hours.
2.
Reading time 10 minutes.
3.
This examination paper has 4 pages.
4.
Total number of questions - THREE (3).
5.
Attempt ALL questions.
6.
Questions are NOT of equal value, total marks
7.
Answers must be written in ink. Except where they are expressly required, pencils
may ONLY be used for drawing, sketching or graphical work.
8.
Candidates may NOT bring their own calculators or computers to the examination.
9.
The following material will be provided by the Examinations Unit:
CASIO fx-911W Calculator.
•
Thermodynamic Properties of Fluids and other data Mayhew and Rogers S.l.
= 100.
10.
This paper may be retained by the candidate.
11.
Candidates may bring drawing instruments to the exam.
For air:
R =
Cp
0.287 kJ/kg
kJjkg
K
kJjkg K
= 1.005 kJ/kg
Cv =
0.718
kJjkg K
kJ/kg
CpjCv = 1,4
k = y = Cp/Cv
All given pressures are absolute
ffJ
QUESTION 1
Part A (10 marks)
A weighted piston!cylinder device contains air at a temperature of 15°C The device has an
initial volume of 0.2Sm3 and an initial pressure of 312kPa.
(i) Calculate the mass of the air within the device in kg.
The device is bought into thermal contact with a reservoir whose temperature is 350°C
until the temperature of the air increases to 175°C The temperature at the system
boundary at the location at which the heat transfer occurs is 350°C
(ii) Calculate the heat transferred to the system in kJ.
(iii) Calculate the change in entropy of the system in kJ/K.
(iv) Calculate the entropy generated during this process in kJ/K.
(v) Calculate the change in entropy of the reservoir in kJ/K.
Assume constant values for R
=
0.287kJ/kg.K and for cp = 1.00SkJ/kg.K.
Part B (15 marks)
Air at an initial temperature of 54SK, an initial pressure of 138kPa and an initial velocity of
32m!
32m1 s flows through an insulated converging nozzle. The pressure of the air exiting the
nozzle is 101.32SkPa. The velocity of the air exiting the nozzle is 287m/s.
287m1s.
(i) Assuming steady conditions write do\VIl the 1st law for this process and calculate the
actual temperature of the air at the exit to the nozzle.
(ii) Calculate the isentropic efficiency of the nozzle and draw the process on a T-s diagram.
(iii) Calculate the entropy generated during this process in kJ Ikg.K.
For air, take R = 0.287kJ/kg.K, cCvv = 0.718kJ/kg.K, cp = 1.005kJ/kg.K and the ratio of
specific heats k = y = 1.40. Assume that the specific heats at constant volume and
pressure remain constant throughout the process.
Part C (10 marks)
An engine operating on the Stirling cycle utilises helium as its working fluid. The gas
constant for helium may be taken as R = 2.0769kJ/kg.K whilst the ratio of specific heats
for helium may be taken as 1.667.
(i) Use this to calculate the specific heats at constant volume
(ii) Draw the Stirling cycle on both a T-s and a P-v diagram
C
Cvv
and pressure cp'
cpo
The maximum temperature that the helium achieves during the cycle is 1750K. At the end
of the isothermal heat addition process, the helium undergoes a constant volume process in
which heat is transferred to the regenerator. The change in entropy during this constant
volume process is S3 - S2 = -S.50kJ/kg.K. You may assume that the values of CCvv and cp
calculate above remain constant throughout the Stirling cycle.
(iii) Determine the temperature of the helium at the end of the constant volume process
and calculate the heat transferred to the regenerator on a per unit mass basis.
(iv) Calculate the thermal efficiency of the cycle.
QUESTION 2 (30 marks)
An engine operating on the dual cycle has a compression ratio (v/v~ of 12.
For the dual cycle,
1-2
2- 3
3-4
4- 5
5-1
Isentropic compression.
Qmstant volume heat addition.
Constant pressure heat addition.
Isentropic expansion.
Constant volume heat rejection.
The temperature at the start of the cycle is 300K and the pressure at the start of the cycle is
100kPa.
Take P
p)3
=
P
P44
=
5J\.1Pa, and Ts
=
600K.
(a)
Draw a P-vdiagram of the dual cycle.
(b)
Calculate the pressure and temperature at each point in the cycle.
(c)
Calculate the ratio (v/v
(v/v))3)
(d)
Calculate the net work and the heat added in kJ/kg
(e)
Calculate the thermal efficiency of the cycle.
(f)
Calculate the changes in entropy for each process in the cycle in kJ/kg.K.
You may assume that the values of cp = 1.005kJ/kg.K and CCvv = 0.718kJ/kg.K are constant
throughout the dual cycle.
QUESTION 3 (35 marks)
An electrical power station is operated using steam in a reheat Rankine cycle. Saturated
liquid water at a pressure of lbar is raised to a pressure of 40bar by a pump. This
pressurised liquid is heated in a boiler lU1til it becomes superheated steam at a temperature
of 450°C The steam is then expanded through a high-pressure turbine to a pressure of
20bar. The isentropic efficiency of the high-pressure turbine is 90%. From there, the steam
is reheated in the boiler until it again reaches a temperature of 450°C and is then expanded
through a low-pressure turbine which has an isentropic efficiency of 92%.
LPTurbine
LP Turbine
+
W
WOlll
OUI
Electrical
Generator
Generator
(a) Find the enthalpies hi, h 2, h 3, h 4s ,' h4a, h s5,, ~s and ~a in kJ/kg, and find the entropies
S2' S3' S4s' S4a' ss,
S5' S6s and S6a in kJ/kg.K. Enter these values in the table below.
SI'
(b) Carefully draw the reheat Rankine cycle process on a T-s diagram.
(c) Write an equation in terms of the enthalpies associated with the steam entering and
leaving the boiler for the total amount of heat transferred <lin
<]m to the steam. Calculate <lin
<]m
in kJ/kg.
(d) Neglecting the power required to circulate the cooling water through the condenser,
write an equation in terms of the enthalpies of the steam entering and leaving both the
high and low-pressure turbines and pump 1 for the net work W net and calculate W net for
the plant in kJ/kg.
(e) Write an expression for the heat transferred qout from the plant and calculate
qout in kJ/kg.
(fj Calculate the thermal efficiency of the plant.
(g) The cooling water entering the condenser is at a pressure of 3bar and a temperature of
20°C The maximum temperature that the cooling water leaving the condenser can be
is 40°C If the mass flow rate of water throughout the plant is 5kg/s, calculate the flow
rate of the cooling water required in kg/s.
(h) Write an expression for the entropy generated
Sgen
in kW/Ko
kW/K.
Sgen
in the condenser and calculate