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VAAL UNIVERSITY OF TECHNOLOGY
FACULTY OF ENGINEERING
DEPARTEMENT: MECHANICAL
NATIONAL DIPLOMA: ENGINEERING: MECHANICAL
SUBJECT:
DATE:
DURATION:
THERMODYNAMICS III
NOV 2008
3 HOURS
EMTGA3-MAIN
EXAMINER: DW SPIRET
MODERATOR: PROF JH WICHERS
REQUIREMENTS:
Steam tables
INSTRUCTIONS:
Assume STP as 101.3 kPa and 15°C unless given
Answer all the questions as instructed
TOTAL: 108
FULL MARKS 100
TfflS QUESTION PAPER CONSISTS OF:
(Properties of Water and Steam)
1 Front Page
2 Typed pages
3 Formulae sheets
DO NOT TURN THE PAGE BEFORE PERMISSION IS GRANTED
VAAL UNIVERSITY OF TECHNOLOGY EMTGA3 2008 NOVEMBER (MAIN)
QUESTION 1
1 kg of air at 100 kPa and 600 K expands according to the law PV^16 = C. The final volume is three times larger than the initial volume.
Draw a P-V and T-S diagram and calculate the work, heat flow and entropy change. [13]
QUESTION 2
In a Joule cycle the pressure ratio is 10 and the upper and lower temperature limits are 773 K and 283 K respectively.
- Draw the P-V and T-S diagrams for this cycle. (2)
- Determine the unknown temperatures. (2)
- Determine the cycle work and the cycle heat. (6)
- Calculate the cycle efficiency and the work ratio for this cycle (2) [12]
QUESTION 3
A single stage compressor has a F.A.D of 5m^3 /min at 15°C and 101.3 kPa. The inlet conditions are 95 kPa and 20°C. The delivery pressure is 500 kPa. The compression index is 1.25 and the clearance volume is 2% of the swept volume. The compressor runs at 1450 rev/min and the stroke is twice the piston diameter.
Calculate: 1 The mass flow of air. (1) 2 The volumetric efficiency. (5) 3 The piston diameter. (5) 4 The power requirement of the compressor. (2) 5 The heat rejected from the cylinder. (2) 6 The isothermal efficiency. (2) 7 Draw a correctly labeled P-V diagram. (2) [19]
QUESTION 4
An eight cylinder 4-stroke engine has a bore of 229 mm and a stroke of 304 mm. The compression ratio is 14/1. The engine develops 500 kW at 750 rev/min. The mechanical efficiency is 90% and the volumetric efficiency is 78%. Fuel with a C.V. of 42 MJ/kg is supplied at an air/fuel ratio of 16/1. The ambient conditions are 100 kPa and 288 K. The IMEP for the pumping loop is 34.5 kPa. The exhaust gas temperature is 450°C and cp for exhaust gasses is 1.135 kJ/kg.K.
Calculate: 1 The brake thermal efficiency. (9) 2 The heat rejected from the engine. (4) 3 The IMEP for the power loop. (4) 4 The efficiency ratio if the cycle is based on the Otto cycle. (2) 5 Draw the P-V diagram for the Otto cycle. (1) [20]
QUESTION 5
A refrigeration plant is required to cool a cold room at -10°C with a cooling load of lOOMJ/h. The refrigerant to be used is Freon 12 (R 12). The refrigerant enters the compressor dry saturated. The temperature of the condensate is 5°C and it is 5°C undercooled. The heat rejected by the condenser is absorbed by water. The temperature rise of the water is 10°C. Assume isentropic compression
THERMODYNAMICS
General formulae
Q+W =AU
m [ Z,g + Vt C,^2 + h, ] +Q + W = m [ Zjg + 14 C 22 + h 2 ] h = u + pv m = CA/v
Vapour Model
U = Uf+X-Ufg S = Sf+Z.Sfg Sfg = Sg - Sf V = Vf + (^) XVfg
Ideal Gas Model
Y = Cv=R/(A.-l) R = cp - cv R = Ro/mo pV = mRT m = n.nio
= 8.3145 kJ.kmol'.K -1^ _v-_
Expansion law V=C PV=C PVn=C P=C
pi/r,=p2^r 2 P.V,=p 2 V 2 P,/p2=[V 2 /V,]n
v,/r,=V2^r 2
T,A' 2 =[V 2 A^l]n-^1 T,/r 2 =Pl/jp 2 *^1
Gas Process
Process Isochoric Isobaric
Isothermal
Isentropic Polytropic
Law V=C p=C pV=C pVY=C pVn=C
AU
w —
AH
AS
cv.ln (T 2 /T,) cp.ln (T 2 /T,) Q/T = R.ln(V 2 /Vi) 0 R.ln (V 2 A^,)+ c.ln (T 2 /T,)
-P(V 2 -V.)
-Glnfa/pj) -CrVj^-V^/Cy-l) (P2VrPiV,)/(n-l)
Q
AU
AH
-W
W[(n-y)/(y-l)l
Vapour Process
Process Isochoric Isobaric
Isothermal Isentropic
Polytropic
Other
Law V=C p=C T=C AS=Q= pVn=C pV=C None
AU AH
Tables Tables Tables Tables Tables
Tables
AS
Tables Tables Q/T 0 Tables
Tables
W
P(V,-V 2 )
AU-Q
AU
(P2V 2 - PlV,)/(n-l) -pV.ln(p,/p 2 ) AU-Q
Q
AU
AH
TAS
-W + AU
-W + AU
Steam plant
"Boiler = msxAh / mfxC.V. ^lpiant = msxAh^rt, / mfxC.V.
E.E. = ms/mf
E.E from & @ 100°C = E.E.xAh/
S.F.C = mf x3600 / (msxAh)
S.S.C. = ms x3600 / (msxAh)
= (tb-tc)/(feed heaters + 1)
Refrigeration
C.O.P= Q /W
C. O. P R E F - T , / ( T 2 - T , )
Reciprocating Compressors
W = nmR(T 2 -Ti)/(n-l)
rP = (P!/P 2 )1/z
Wis0 = mRTln(P 2 /Pi)
Tlvoi = v/vs = l+(V
