engineering questions and answers
TRANSCRIPT
-
7/23/2019 Engineering Questions and Answers
1/35
1
-QUESTIONS AND ANSWERS ES180 ENERGYUNIT 1
1. Which of the following are closed systems?
a) A block of woodb) The gas within a cylinderc) The volume enclosed by a car exhaustd) The gases within a car exhaust at some instant in timee) The Universef) Steam coming from the spout of a kettle
[ a, b, d, e.]
2. Which of the following are simple systems?
a) Compressed hydrogen in a cylinderb) Air and water vapour above liquid water in a corked
bottlec) An
iron bard) A sample of exhaust fumes (carbon monoxide, nitrogen,
carbon dioxide etc taken from a car exhaust
e) Air in the cylinder of a compressor
[ a, e. c can be argued over. If the bar is only subjected toforce along its length, and varying temperature then it canbe regarded as a simple system with say force a functionof temperature and length.]
3. Which of the following are independent variables?
a) The pressure and. volume of a mass of gasb) The pressure and specific volume of a mass of gasc) The volume and specific volume of a mass of gas
[ a, b.]
-
7/23/2019 Engineering Questions and Answers
2/35
2
UNIT2
1. What is the work done by the system (W) in the cases below:
Force F moves x
Force F
System
System
Moves xhorizontally
(a)
(b)
(c)
zm System falls
from ledge toground
(d)
System m
Spring
Initial spring force =0Final spring force = mgdistance moved = z
a) -Fx
b) - FxCosc) 0d) mgz/2
2. An ideal mechanism has 20J of work done on it by a spring, 50J
of work done on it by a hydraulic ram, and 30J done on it by theimpact of a hammer.
What is its work output?
[ 100J]
-
7/23/2019 Engineering Questions and Answers
3/35
3
Unit31. An ideal electric motor consumes 30 amps at 240 volts for 10
seconds. What is the electrical work and mechanical work?[Electrical work (on system) = -72kJMechanical work (by system) = 72kJ]
2. A sinusoidally varying a.c. supply has an r.m.s. voltage of 240 V.What is the peak voltage?339 V = 1.414 x 240 V rms
3. An ideal generator is driven by a shaft rotating at 1400 r.p.m. Thetorque on the shaft is 20 Nm. If the output voltage is 240 V rms,what is the delivered current?
amps2.12
240260
140020
=
=
=
I
I
IVT rmsrms
4. A manufacturer of electric fires claims that the power of one oftheir products is 3kWh. Why is this meaningless?
5. An ideal electric motor has a voltage supply of 415 V rms and
consumes 5 amps rms, its power factor being 0.8. If it runs for oneminute, what is the quantity of mechanical work that it will havedelivered?415 x 5 x 0.8 x 60=99600 J=99.6 kJ
-
7/23/2019 Engineering Questions and Answers
4/35
4
6. An ideal electric motor has an output of 2 kW. If it drives a loadfor 3 hours, what is the total energy delivered to its load, a) in kWh,b) in MJ?6 kWh, 21.6 MJ
7. An ideal transformer steps down a supply voltage by a factor of12. If the supply voltage is 1200 V rms and it consumes 20 A, whatare the output voltage, current and power?
100 V, 240 A, 24 kW
Unit 4
1. What is the net heat transfer of the following systems:
a)
100 J
500 J
300 J
200 J
100 J
500 J of work
300 J
200 J
1 kJ
500 J
100 J
600 J
b)
c)
SYSTEM
SYSTEM
SYSTEM
[a) -500 Jb) +200J (the work transfer is irrelevant.c) 0]
2. Why is it meaningless to say that 50C is twice as hot as 25C?The statement could only have a meaning if the temperature scalewere an absolute one.
-
7/23/2019 Engineering Questions and Answers
5/35
5
3. What is 170C in Kelvin?K = 273 + C = 273 170 = 103 Kelvin
4. What is 373 K in C?C = K 273 = 373 273 = 100C
5. What is 100C in F?F = 32 + 9/5 C = 32 + 180 = 212F
6. At what temperature are the Celsius and Fahrenheit scales
numerically equal?F = 32 + 9/5 CX = 32 + 9/5 X
X = - 32 x 5/4 = - 40 (C or F)
UNIT 5
1) A cyclic device (an engine) takes in 100J of heat andproduces 20J of work. What is the heat output andefficiency?[80J, 20%]
2) A petrol and air mixture in a closed rigid and insulatingcylinder spontaneously ignites. Does the internal energy ofthe mixture decrease, increase or remain steady?[steady]
3) A mass of gas in a closed insulated cylinder has aninternal energy of 10 kJ (State 1). It is compressed to State2, the work input being 1 kJ, and then cooled to State 3, 5kJ of heat being removed. What is the final internalenergy? Would it be different if the two processes wereperformed in the opposite order?[6kJ, No]
-
7/23/2019 Engineering Questions and Answers
6/35
6
4) Insert +, - , or 0 for Q, W, E in the fol lowing below. Thesystem is defined by underlining. Make reasonableassumptions.
Process Q W E
Air in a cylinder is compressed bymoving a piston. The piston andcylinder are nonconducting
A body is released in vacuo andfalls
The body then strikes a rigidnonconducting horizontal planeand comes to rest
Air in a balloon expands in thesunshine
A battery - driven vehicle climbs upa rock on the moon
A bowl of water at 0 C and 1atmosphere in a refrigeratorfreezes
A non - conducting rough blockslides at steady speed down a rigidinclined plane
Q W E
1 0 - +
2 0 0 0
3 0 0 04 + + +
5 0 0 0 Chemical energytransformed into potentialenergy. Both contribute toE.
6 - + - Freezing water expands,doing work.
7 +?or -? + Energy to plane could bework or heat.
-
7/23/2019 Engineering Questions and Answers
7/35
7
5) A wire is kept at ambient temperature while it is stretched by lmby a force which rises from zero to 1000N according to HookesLaw (force proportional to extension). Its length if then fixedwhile it receives 30,000 J of heat and its tension falls to zero. Itis released and returns at zero tension to its original state while
losing 31,000 J of heat. Tabulate W, Q, E for all threeprocesses.
W (out) Q (in) EP1 [1] 500 ( x 1000 x 1) [11] 500 [10] 1,000
P2 [2] 0 [5] 30,000 [7] 30,000
P3 [3] 0 [6] 31,000 [8] 31,000
TOTAL [4]-500 [12] -500 [9] 0 (cycle E = 0)
6) A heat pump takes in 2000 J of heat and 1000 J of work. Whatis its COP? What would the COP be if it were a refrigerator?
[3,2]
7) A sample of gas exerts a steady gauge pressure of 130 kPa ona piston of diameter 0.25m which advances 0.l6m. How muchwork is done by the gas if the barometer reads 760mm Hg?[Note that the density of mercury is 13,600 kg/m3.]
Atmospheric pressure = 13,600 x 9.81 x 0.76 = 1.0140e+005Pa = 1.0140 bar a.Gas pressure = 1.0140e+005 + 1.3 e+005= 2.3140e+005 Pa
Work done = p V= 2.3140e+005 x (0.25/2)
2x x 0.16
= 1.8174e+003 J= 1.8174 kJ
-
7/23/2019 Engineering Questions and Answers
8/35
8
8) 0.5m3of gas at an initial pressure of 6 bar is slowly expanded
and heated so that pV is constant. If its final volume is l.0m3what is the work done?
( )
( ) kJ2ln300
Joules2ln103
103
1035.0106ande)(Reversibl
5
1.0
5.0
5
55
=
=
=
===
V
dV
pVpdVW
9) A kilogram of gas, obeying the relation u = 2pv is confinedbehind a piston in a cylinder. Evaluate Q and W for the gas inthe following reversible processes, and sketch and label themon a p - V diagram.
Process:a) Constant volume = v0. Pressure rises from p0to 2p0
b) Constant pressure = 2po. Volume falls from v0to v0/ 2.c) u = 2p0v0(constant). Pressure rises from p0to 2p0(You will need to consider what the p V relationship is)
d) Same overall change of state as in (c) but achieved by aconstant volume process followed by a constant pressure
process.
-
7/23/2019 Engineering Questions and Answers
9/35
9
p
V o
2p0
p0
v0v /20
a
b
c
1
2
3
State 1: p = p0 v = v0 u = 2 p0v0
State 2: p = 2p0 v = v0 u = 4 p0v0State 3: p = 2p0 v = v0/2 u = 2 p0v0
Process a: 1 to 2
U = 2 p0v0and W = 0 (v constant)
Q = W + U= 2 p0v0
Process b: 2 to 3
00
0000
00
00
0
3
2
0
3
2
3
2
)2
(2
2
vp
vpvp
UWQ
vp
vvp
dVp
pdVW
=
=
+=
=
=
=
=
-
7/23/2019 Engineering Questions and Answers
10/35
10
U = -2 p0v0
Process c: 3 to 1
U = 0
Q=W
( )
2ln
2ln
2lnln
00
00
0000
1
300
1
3
vpQ
vp
vvvp
v
dv
vp
pdvW
=
=
=
=
=
d ) Sum a and b
10) An engine cycle has a p - V diagram as below. What is thework done per cycle? If the gross heat input/cycle is l44kJ,
what is the engine effic iency? How much heat is rejected(ie output) per cycle?
-
7/23/2019 Engineering Questions and Answers
11/35
11
N.B. 1 bar = 10 Pap
V
10 bar
1 bar
0.01 m3
0.09 m3
IF reversibleW=1/2 x (9 x 105) x 0.08 J/cycle= 36 kJ
= 36 / 144 =0.25
Q= W for cycle:QIN QOUT= WNET144- QOUT= 36QOUT= 108 kJ
11) If the p -V diagram of Qu10 were an indicator diagram of a2-cylinder engine rotating at 1000 rpm and one cycle js
executed by one cylinder for every revolution, what is theindicated power?Indicated power = work/cycle x cycles / sec. = 36 x 2 x
(1000/60) = 1200 kW
11) Oil flows in a pipeline at a rate of 3 m3s-1and the pressuredrop is 40 Pa per metre of length. What is the minimum
electrical power required to pump the oil 20 km? Why isthis a minimum?
-
7/23/2019 Engineering Questions and Answers
12/35
12
Power = 3 x 40 x 20,000 = 2,400,000 W ( )pVW = &&
= 2.4 MW
This is a minimum because it assumes the pump is 100%efficient.
12) Air flows through a heat exchanger at a rate of 50 litres persecond. The pressure drop is 50 Pa. What is the minimumpower required to maintain the air flow? If the fan andmotor assembly driving the air has an efficiency of 60%and the motor has a 240 Vac supply, how much current is
drawn by the motor?
mA4.17
01736.0
2400.6
2.5
Watts5.2
50)1000/50(
=
=
==
=
=
=
rms
rmsrmsrms
I
IIV
pVW &&
13) What is the power loss of a wire of resistance 200
when
carrying 12 A?
kW8.28
800,282001442
=
==RI
14) A normal domestic 240Vac power point has a 13 A fuse.What is the maximum power that can be drawn from it?What would be the corresponding resistance of the load?
-
7/23/2019 Engineering Questions and Answers
13/35
13
13A x 240V = 3120 W= 3.12 kW
3120 = (13)2R
R = 18.5
15) A closed cycle gas turbine has a heat input of 1 MW and aheat output of 850 kW. What is its power output andefficiency?
QIN=1000 kW QOUT= 850 kW
W = 150 kW (
Q = W)Turbine
15.01000150
kW150
8501000
cycleforLawFirst
==
=
=
=
netW
QW &&
16) A refrigerator consumes 100W of electr ici ty and 250W ofheat is rejected from the machine to the environment. Whatis i ts COP?
WIN=100 W QOUT= 250 WRefrigerator
QIN= 150 W (Q = W)
COPREF= QIN/W =1.5
-
7/23/2019 Engineering Questions and Answers
14/35
14
UNIT 6
1. An electric kettle contains 3.5 litres of water at 15C.
Neglecting any heat loss, how long will it take for the contentsto reach 95C if the heating element within it is rated at 3 kW?
3 x time = 3.5 kg x 4.2 kJ/kg K x (95-15)Time =392 s
2. A solar heating system has an energy store consisting of 5 m3of hot water. When needed, energy is drawn from it at a rate of
5 kW, the initial temperature being 80C and the final usabletemperature being 35C. How much energy can be removed,and how long does it take, should no energy be available toreplenish the store?
Energy removed = m cpT= 5000 kg x 4.2 kJ/kg K x (80-35) [kJ]= 945 MJ
945,000 kJ / 5 KW= 189000 s= 52.5 hours
3. An elastic spring is compressed from its unloaded state to onewhere the force on it is 10 kN, during which time the springreduces in length by 0.1 m. How much energy is stored?
Strain Energy = x 10,000 x 0.1 [J]= 500 J
4. A flywheel energy store with moment of inertia about its axis ofrotation of 15 kg m2is initially rotating at 14000 rpm. Howmuch energy is removed if the speed is reduced to 3000 rpm?
E = I (2final- 2initial)
= 15 [(3000 x 2/60)2
-(14000 x 2/60)2
] J= - 15.4 MJ
-
7/23/2019 Engineering Questions and Answers
15/35
15
5. It is proposed that a house have its own pumped storage
system (a micro-Dinorwic). Make some estimates of likelystore volumes and pumping heights to get an estimate of howmany kWh of electricity could be stored. How long could itpower a colour TV that consumes 150 W?
Volume = 5m x 4m x 1m = 20 m3
Mass = 20 000 kg
Head = 5m
P.E. = mgh = 20 000 x 10 x 5 J = 1 MJ approx.Assume 25% losses in energy conversions and 750 kJ ofelectricity can be stored.
Time = 750 000 / 150 / 3600 hours
= 1.4 hours [Not a lot!]
-
7/23/2019 Engineering Questions and Answers
16/35
16
UNIT 7
Write down (but do not solve) the SFEE for the followingsituations. Fluid velocities are negligible unless otherwise
stated.
a)
m kg/sec m kg/sech1 kJ/kg h2 kJ/kg
Fluid Heater
Q kWb)
m kg/sec m kg/sech1 kJ/kg h2 kJ/kg
W kW
Q kW (+ve number)c)
m kg/sec m kg/sech1 kJ/kg h2 kJ/kg
c1m/s c2m/sW=0
Q =0
d) __________
__________h2kJ/kg, m kg/s, c2 m/s, height z
______
h1kJ/kg, m kg/s, c1 m/s, height 0 __________
Expander
Diffuser
Water Pump
Q =0 W kW
Apply SFEE : Q = W + m[ (h2 h1) + (c22 c1
2) + g (z2 z1) ]a) Q = m(h2 h1)b) Q = W + m(h2 h1)c) 0 = 0 + m[ (h2 h1) + (c2
2 c12)]
h must be in Joules/kg
d) 0 = -W + m[ (h2 h1) + (c22
c12
) +gz]
-
7/23/2019 Engineering Questions and Answers
17/35
17
UNIT 8
PERFECT GASESGiven: R0 = 8314 J/kg mol K
Air: MW = 29, = 1.4Calculate:
1) The Gas Constant of air.R = Ro/MW = 8314/29 = 287 J/kg K
2) cpfor air
cp= R / (-1) = 1.4 x 287 / 0.4
=1005 J/kg K
3) The specific enthalpy of air at 20C (Take zero enthalpy as beingat 0 K).
h = cpT = 1005 x 293= 294465 J/kg= 294 kJ/kg
4) cvfor aircv= R / (-1)= 287 / 0.4=718 J/kg K
5) u for air at 20 Cu = cvT = 718 x 293= 210 kJ/kg
6) 5 kg of air in a rigid vessel is heated from 20C to 80C. Howmuch heat is required?
Q = U = m cvT= 5 x 0.718 x (80 - 20)= 215.4 kJ
-
7/23/2019 Engineering Questions and Answers
18/35
18
7) 5 kg of air per second passes through a heater, which raises its
temperature from 20C to 80C. What is the heat input power?Q = H = m cpT= 5 x 1.005 x (80 20)= 301.5 kW
8) In Qu. 6, what is the final air pressure assuming that the initialpressure is 2 bar a? [ 2.41 bar]
( ) ( )abar41.2
27380273202
lawgasPerfect
2
2
2
22
1
11
=
+=+
=
p
VpV
T
Vp
T
Vp
9) In Qu. 7, what is the final air pressure assuming that the initialpressure is 2 bar a?
2 bar a no change
CONDENSIBLE GASESFor saturation properties of water and steam use pages 2,3 of thetables for pressures up to 1 bar, saturation temperatures up to100C. For higher pressures and temperatures use pages 4 and 5.Superheated properties are on pages 6,7,8.
10). What is the enthalpy of 3 kg of saturated water at 60C?
H = mh = 3 x 251.1= 753.3 kJ
11) What is the specific internal energy of saturated steam at 0.5bar? What is its temperature, i.e. boiling point?
2483 kJ/kg, 81.3C
12) What is the Latent heat i.e. enthalpy of vaporisation of water at40C? 2406.2 kJ/kg
-
7/23/2019 Engineering Questions and Answers
19/35
19
13) If the specific enthalpy of steam at 40 bar is 1500 kJ kg-1, whatis the dryness fraction?
x = (h h f ) / hfg= (1500 1087) / 1714= 0.241
14). If the dryness fraction of steam at 0.1 bar is 90%, what is itstemperature and internal energy?
45.8 C [page 3]u = 0.1 uf+ 0.9 ug or = uf+ 0.9(ug uf)= 0.1 x 192 + 0.9 x 2437= 2212.5 kJ kg-1
15) Using tables, find the values of the following properties of
superheated steam.a) p = 5 barb) p = 1.5 barc) p = 15 bard) p = l0 bar
e) p = 7 barf) p = 8.3barg) p = l0 barh) p = 0.5 bari) p = 20 bar
j) p = 6.5 bar
T = 350CT = 400CT = 400CT = 375C
T = 312CT = 250Ch = 3000 kJ/kgh = 3000 kJ/kgs = 7.1 kJ/kg KT = 310C
u=?h= ?h= ?v= ?
h= ?h= ?T= ?T= ?T= ?h=?
Answer to 15
a) 2883 kJ/kg Direct from tables.b) 3277 kJ/kg Direct from tablesc) 3256 kJ/kg Direct from tablesd) 0.2945 m3/kg
( )
( )
2945.0
2825.03065.0
50
252825.0
2825.03065.0350400
3503752825.0
=
+=
+=v
-
7/23/2019 Engineering Questions and Answers
20/35
20
e) 3085 kJ/kgh = 3060 +12/50 (3164 3060)
= 3060 +24.96= 3084.96 kJ/kg
f) 2950 kJ/kgh = 2951 + 0.3/1 (2948 2951)
= 2951 0.9= 2950 kJ/kg
g) 275.9
CT= 250 + 50 (3000 2944) / (3052 2944)
= 250 +50 x 0.5185= 250 +25.9
=275.9
C
h) 262
CT= 250 + 50 (3000 2976) / (3076 2976)
= 250 +50 x 0.24
=262
C
i) 392
CT= 350 + 50 (7.1 6.957) / (7.126 6.957)
= 350 +50 x 0.846= 350 +42.3= 392C
j) 3081.8 kJ/kgh6.5, 300= 3061h6.5, 350= 3165h6.5, 310= 3061 + 10/50 (3165 3061)
= 3061 + 20.8= 3081.8 kJ/kg
-
7/23/2019 Engineering Questions and Answers
21/35
21
UNIT 91) An adiabatic nozzle takes in steam at negligible velocity, 10 bar,
and 4000C. The exit steam is at 2 bar and 2000C. What is itsvelocity? [886.6 m/s]
1 2
10 bar
400 C
c =0
o
1
2 bar
200 C
c =?
o
2
h1 = 3264 kJ/kg h2 = 2871 kJ/kg(c2
2 c12) = h1 h2 hs in J/kg
c22= 1000(3264 2871)
c22= 768000
c2= 886.6 m/s
2) A boiler evaporates 5 kg/sec of steam at 20 bar. What is the heatinput? The inlet enthalpy is 605 kJ/kg and outlet enthalpy is2799 kJ/kg. [10.97 MW]
h1 = 605 kJ/kg h2 = 2799 kJ/kg
Q=?
Boiler
Q = m (h2h1)= 5 (2799 605)= 10,970 kW= 10.97 MW
-
7/23/2019 Engineering Questions and Answers
22/35
22
3) A superheater takes 5 kg/sec of saturated steam at 20 bar, andheats it to 3500C. The inlet enthalpy is 2799 kJ/kg. What is theheat input? [1.695 MW]
h1 = 2799 kJ/kg h2 = ? kJ/kg
20 bar, 350
CSuperheater
Q=?
h2 = 3138 kJ/kgQ = m (h2h1)
= 5 (3138 - 2799)= 1695 kW= 1.695 MW
4) A turbine takes in 5 kg/sec of steam at 20 bar and 3500C. The
outlet conditions are 4 bar and 2l0C. How much work isproduced? [1.277 MW]
h1 = 3138 kJ/kg h2 = ? kJ/kg
(20 bar, 350
C)
W ?
Turbine
h2= 2862 +10/50 (2965 2862 )= 2882.6
W = m (h1 h2)= 5 (3138 2882.6)= 1277 kW=1.277 MW
5) A desuperheater and condenser take 5 kg/sec of steam at 4
bar and 210C and cool the fluid to produce liquid water withan enthalpy of 605 kJ/kg. What is the heat output? [11.388
MW]
-
7/23/2019 Engineering Questions and Answers
23/35
23
h1 = 2882.6 kJ/kg h2 = 605 kJ/kg
Q ? (-ve)
Desuperheater+ Condenser
Q = m (h2h1)= 5 (605 2882.6)= -11,388 kW= -11.388 MW
6) The boiler of Qu.2, superheater of Qu.3, turbine of Qu.4,desuperheater and condenser of Qu.5, are combined in asteam turbine plant as shown below. What is the total heat
input, work output, heat rejected and efficiency? [12.665MW,1.277 MW, 11.388 MW, 0.1008]
Qin
Qout
W
Sat. steam20 bar
H.P.Water
Boiler Superheater
Turbine
Feed pump toreturn water to20 bar. Small
work input. Desuperheaterand condenser
Superheatedsteam at 20 bar
Superheatedsteam at 4 bar
Gross heat in = Heat to boiler + Heat to superheater
=10.97 + 1.695 = 12.665 MW
Net work out from turbine (feed pump neglected) = 1.277 MW
Heat rejected = Heat in Work out= 12.555 1.277 = 11.388 MW ( or directly from Qu.21)
= Net Work / Heat in = 1.277/12.665 = 0.1008
-
7/23/2019 Engineering Questions and Answers
24/35
24
7) Air at 10C and 80 kPa enters the diffuser of a jet engine with avelocity of 200 m s-1. The inlet area is 0.4 m2. The outlet velocityis small compared to the inlet velocity. Calculate a) the mass
flow rate, b) the exit temperature. [78.8 kg s-1, 29.9C]
CT
T
T
Tchc
AcRT
pAcm
exit
p
o
p
2
2
1-
9.29
9.19
kJ/kgKnotKJ/kgincNote1005200
2
1
2
1
skg79.782004.0283287
80000
=
=
=
==
=
=== &
8) A heat exchanger transfers heat from a steady stream of oil to asteady stream of water without heat loss to the surrounds. The
flow rate of the oil is 0.1 kg s-1
, its inlet temperature is 180C,
outlet temperature 90C and its specific heat is 800 J kg-1
K-1
.The water, specific heat 4.2 kJ kg
-1 K
-1enters at 40C with a
mass flow rate of 0.03 kg s-1 . What is the heat flux and the
outlet temperature of the water? [7.2 kW, 97C]
( ) ( )( ) ( )
( ) (( )
C1.971.5740
40420003.0Watts720040420003.0901808004.0
o=+=
====
==
==
out
out
out
waterpoilp
wateroil
T
TQTQ
TcmTcm
HHQ
&
&
&&
&&&
)
9) A throttle reduces the pressure of a stream of a perfect gasfrom 40 bar to 1 bar. Does the temperature a) go up, b) godown, c) remain the same?
h = cpT= constant, so Tis constant
-
7/23/2019 Engineering Questions and Answers
25/35
25
10) The compressor of a gas turbine power plant compresses
3 kg s-1air (cp= 1.005 kJ kg-1K-1) from 1 bar, 300K to 4 bar,
446 K. What is the work input? [440 kW]
( )
( )kW440
300-4461.0053
ally)convention(notnumberpositiveaasExpressed
=
=
= inoutp TTcmW &&
11) The combustion chamber of the same gas turbine adds heat at
a rate of 2.9 MW to the air. What is the exit temperature? [1408
K]
( )
( )
C1408
446-1.00532900
o=
=
=
out
out
inoutp
T
T
TTcmQ &&
12) The turbine of the same plant expands the air back to 1 bar, the
exit temperature being 948 K. What is the power output? [1.39MW]
( )
( )
kW1387
948-14081.0053
=
=
= inoutp TTcmW &&
13) What is the efficiency of the complete plant? [0.33]
33.02900
4401387 === inQW
14) Air (density 1.225 kg m-3
) enters a duct of cross sectional area0.3 m
2with a speed of 10 m s
-1. Its static pressure is 1 bar a. If
the flow in the dust if frictionless and incompressible, and theoutlet has a cross-sectional area of 0.1 m
2, determine the mass
flow rate, the exit speed, the exit static pressure and exit
dynamic pressure. [3.675 kg s-1, 99.51 kPa, 551.25 Pa]
-
7/23/2019 Engineering Questions and Answers
26/35
26
( )
( )
( )
Pa25.551
2
1dynamicExit
kPa99.51Pa99510490100000
static-inletstaticexitSo
Pa490
1030225.12
1
Bernoulli)-constantpressure(Totalpressuredynamicpressurestatic
sm30103
1.0225.1
skg675.3103.0225.1
2
22
1-
1
=
=
= ==
=
=
=
====
==
===
c
cA
A
c
cAcm
Acm
inout
in
out
outiout
in
&
&
UNIT 10
1. An eight cylinder four-stroke engine rotates at 3600rpm,producing 50kW shaft power. What is the work done percylinder per cycle? If the engine is 25% efficient, what is theheat input per cycle? [208 J, 832 J]
Cycles/s = 3600 / 60 / 2 = 30 [2 revolutions per cycle]Work/cyl/cycle = 50kJ/s / 30 cycles/s / 8 cylinders
= 208 J
Heat in = 208/0.25 = 832 J
2. A single cylinder two-stroke engine produces 3 kW of shaftpower at 4000rpm, its efficiency being 20%. How much heat isrejected per cycle? [180 J]
Cycles/s = 4000 / 60 / = 66.7 [1 revolution per cycle]Work/cycle = 3000 W / 66.7 = 45 J
Heat REJECTED = 45 / 0.2 45 = 180 J
-
7/23/2019 Engineering Questions and Answers
27/35
27
3. An ideal simple gas turbine has a compression ratio of 5. Whatis its efficiency? If the turbine produces 6 MW (gross) and thecompressor requires 2 MW to drive it, what is the work ratioand how much heat is rejected? [0.369, 0.667, 6.84 MW]
MW6.844-10.84rejectedHeat
WM84.10369.0
4inHeat
32
626
outWork
(-ve)inworkoutWork
369.05
11
11
4.1
4.01
==
==
==
+=
=
=
=
w
p
r
r
4. What is the efficiency of an ideal diesel engine with acompression ratio of 20 and a cut-off ratio of 3? [61%]
( ) ( )
606.0
134.1
13
20
11
1
111
4.1
4.01
=
=
= c
c
v r
r
r
-
7/23/2019 Engineering Questions and Answers
28/35
28
UNIT 11/12
1. a)A single stream of fluid enters and leaves the devices listed in the Table.Fill in the missing boxes.
Device Heat flow[ +, - , 0
(adiabatic) ]
Reversible?[Yes, No, Either]
Outlet S InletS
[+, -, 0 or any]
Compressor 0 Y 0
- Y -
0 N +
- N any
0 Y 0
Turbine 0 Y 0- Y -
0 N +
+ Y +
0 Y 0
Heater + Y +
+ N +
Nozzle 0 Y 0
0 N +
- Y -
b) A closed cyclic engine takes in a positive net amount of heat. It isirreversible. Does its entropy increase, decrease or remain constant?
[Constant it is a cyclic device so after each cycle the properties (includingentropy) of all parts of it are returned to their initial values. However, theentropy of the sources and sinks of heat in thermal communication with it willhave increased.]
2. A large body at 200C loses 6 kJ of heat. What is its change in entropy?
J/K68.12273200
6000=
+
==
=
T
QS
STQ
-
7/23/2019 Engineering Questions and Answers
29/35
29
3. A large body is at 600K. The entropy increases by 4 kJ/K. How much heattransfer has there been and in which direction?
body)(intokJ2400
kJ/K4600
=
=
= STQ
4. As question 3 but there is also 6 MJ of work done on the body.
[No difference the work is irrelevant.]
5. A Carnot cycle engine takes in heat at 1000C and rejects heat at 20C.What is its efficiency?
%771273
29311 ===
H
CCarnot
T
T
6. An ideal reversible engine takes in heat at 200C and rejects heat at 0C.What is its efficiency?
%42473
27311 ====
H
CCarnot
T
T
7. An inventor claims to have an engine that takes in a steady10 kW of heatfrom steam at 100C, rejects heat to the environment at 20C and has asteady 3 kW work output. Do you believe her/him?
not.doINoi.e.%22373
2931possibleMaximum
%30
===
=
Carnot
Claimed
-
7/23/2019 Engineering Questions and Answers
30/35
30
8. A heat pump uses 2 kW (continuous) of electricity, extracts heat from theenvironment at -3C and delivers heat to a house at 27C. What is themaximum possible heating power delivered?
1030
300
secin /Workout /secHeat
==
=
=CH
HCarnot
TTTCOP
So 2 x 10 = 20 kW is maximum output.
9. A cyclic Carnot refrigerator takes heat from a large body at 200 K and
delivers it to the environment at 300 K. For each kJ of work consumed,calculate the cooling, the change in entropy of the cold body, the heatrejected and the entropy change of the environment. What is the entropychange of the refrigerator, the cold body and the environment takentogether as a single system?
0So
(cyclic)0
J/K10
300
3000
J/K10200
2000
kJ3rejectedHeatsokJ,2CoolingkJ,1Work
2200300
200
inputWork
CoolingRe
=
=
+===
=
==
===
=
=
=
=
All
orrefrigerat
hot
hot
cold
cold
CH
Cf
S
ST
QS
T
QS
TT
TCOP
-
7/23/2019 Engineering Questions and Answers
31/35
31
10. A heating installation consists of a heat engine that takes in heatfrom a coal furnace at 600K, driving a heat pump, which takes inheat at 300K from the surroundings. Both devices deliver heat at375K to a building. By applying the First Law and the ClausiusInequality to the whole installation find the upper limit for the ratioof heat delivered to the building to the heat supplied by thefurnace. Under what conditions would this limit be reached?What would be the answer if the engine rejected its heat to thesurroundings at 300K instead of the building at 375K? Whichinstallation would you select?
Engine HeatPum
WQH
375 K
QM
QC
300 K
600 K
For the whole system (in dotted box) the First Law is:
QC- QM+ QH= 0Clausius Inequality:
0
0
=+
H
H
M
M
C
C
T
Q
T
Q
T
Q
T
Q
-
7/23/2019 Engineering Questions and Answers
32/35
32
5.2
375
1
300
1
600
1
300
1
11
11
11
11
1111
01111
0
+
+
++
+
H
M
H
M
MC
HC
H
M
MC
HC
H
M
HC
H
MC
M
HC
H
MC
M
H
H
M
M
C
HM
Q
Q
Q
Q
TT
TT
Q
Q
TT
TT
Q
Q
TTQ
TTQ
TTQTTQ
T
Q
T
Q
T
QQ
Equality holds if everything is reversible.
The same answer holds if heat rejected to environment, becausemore efficient engine makes up for lack of waste heat to building,but this would involve larger heat exchangers and be moreexpensive.
-
7/23/2019 Engineering Questions and Answers
33/35
33
11. A heat pump takes in 600J of heat at 27C while rejecting heat toa system whose temperature rises 1C for each joule supplied toit. Initially the system is also at 27C. Show that there is a limit tothe final temperature of the system and calculate its value. Is itan upper or lower limit? Under what conditions would it bereached? [This requires an integration, since the systemchanges in temperature during heating a more difficultproblem]
600 J300 K
System1 J/K
300 K initially
Heat
Pump
dQ = c dTand c= 1, sodQ = dTClausius for Heat pump:
[ ]
K2217
2300
ln
ln20
20
300
6000
0
300
final
final
Tfinal
T
T
TT
dT
T
dQ
TQ
-
7/23/2019 Engineering Questions and Answers
34/35
34
UNIT 131. How much heat is conducted along the length of a 100 mm
long 5 mm diameter copper rod if one end is at 0C and theother end is at 100C? k for copper is 386 W m-1K-1.
W6.7
1.0
1000025.0386 2
=
=
=
x
TkAQ&
2. How much heat would be transmitted if the rod were stainlesssteel, k = 16 W m
-1K
-1?
W31.0
1.0
1000025.016 2
=
=
=
x
TkAQ&
3. A furnace wall is composed of an inner layer of refractory, 200mm thick, k = 1.1 and a stainless steel outer covering, 3 mmthick. The internal heat transfer coefficient is 100 Wm-2K-1andthe external heat transfer coefficient is 15 Wm
-2 K
-1. If the
furnace approximates to a 1 m cube, the internal temperature
is 900C and the external temperature is 50C, what is the rate
of heat loss? What is the temperature of the outer surface ofthe stainless steel? [Use the heat flux and the external heattransfer coefficient to obtain this]
21
21
11
fb
b
a
a
f
ff
hk
x
k
x
h
TTAQ
+++
=&
-
7/23/2019 Engineering Questions and Answers
35/35
35
( )
W19716
100
1
16
003.0
1.1
2.0
15
1
509006
=
+++
=Q&
This is also the heat through the external boundary layer, whichseparates the external air temperature and the steel surfacetemperature.
( )
( )
C269
21950
5061519716
o=
+==
=
steel
steel
Outsidesteel
T
T
TThAQ&