engineering questions and answers

7/23/2019 Engineering Questions and Answers

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-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.]


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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]


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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


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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.


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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]


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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.


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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


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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.


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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

=

=

+=

=

=

=

=


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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?


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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?


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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?


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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


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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


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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!]


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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)


W kW

Q kW (+ve number)c)


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]


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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


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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


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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


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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


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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


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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]


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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


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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


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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]


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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


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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


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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


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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


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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


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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


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.


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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


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

+++

=&


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&

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