problems on gas cycles in thermo

8/12/2019 Problems on Gas Cycles in thermo

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Problems on Gas Cycles:

1. An automobile engine consumes fuel at a rate of 28 L/h and delivers 60kW of po er to the heels. !f the fuel has a heating value of ""#000 k$/kgand a densit% of 0.8 g/cm determine the efficienc% of this engine.

Solution:

2. 'onsider an ideal (ricsson c%cle ith air as the orking fluid e)ecuted in

kg22."L/h*kg/L*+28+0.8*,+m fuelfuel === 2-&.-8k$/h8 #600k$/kg*00kg/h*+""#0+22."um coalcoalA ====

A

net

QW

e = 21.or0.21

2-&.-8kW

60kW ==


2/13

a stead% flo s%stem.Air is at 2-3' and 120

k4a at the beginning of the isothermal compression process# during hich1 0 k$/kg of heat is re5ected. eat transfer to air occurs at 1200 7.

etermine + a* the ma)imum pressure in the c%cle# + b* the net ork output per unit mass of air# and + c* the thermal efficienc% of the c%cle.

9olution:

a*

;hus#

kPa

kP P

K kg kJ K kg kJ

T

T

RT

T

c s

Kkg kJ K

kg kJ T

q s

p

2.68

120ln*/28-.0+/.0

lnln

/.0&00

/1 0

"

"

&

"

&

"

&"

1

"&&"

=

==

=== kJ kg kJ K K

QT T

QT T

QQ

R A A

R /600*/1 0+&00

1200*

&

1

1

& ====

kkJ QQw R Anet /" 01 0600 ===


3/13

&.


4/13V

V pp

V pV p

Then

mRT V p

mRT V pT T

V mRT W

vv

mRdV V

mRT pdV W

QW

kJ Q

h

h

11.-2&60

@ *&.0*+6.+

#

A

.02&81.0n

"0

1

221

2211

22

1121

121

1

2

2

1

2

121

2121

21

====

===

====

===

==


5/13

'.* =or process 2 &

=or process & "

=or process " 1

0&2 =

Q

*+ &2&2 uumW =

kkg W -.2 6*0.16--."2&+1&2 ==

"&"& = QW

W kkJ QkJ kJ QT

QT

Q

hc

1#1616*"0+".0BBBBB

"&"&"&21"& ======


6/13


7/13

b.*

. 'onsidera simple ideal ?ra%ton c%cle ith air as the orking fluid. ;he pressure ratioof the c%cle is 6# and the minimum and ma)imum temperatures are &00 and

1&00 7# respectivel%. Do the pressure ratio is doubled ithout changingthe minimum and ma)imum temperatures in the c%cle. etermine thechange in + a* the net ork output per unit mass and + b* the thermalefficienc% of the c%cle as a result of this modification. Assume variablespecific heats for air.

9olution:

=or > 6

kg kJ kg kJ K K

qT T

eqw A Anet /-2*/00+1800& 0

111

& =

===

kkJ h K T /1.&00&00 11 ==

&86.11 =r P kkJ h K T /-.1&1&00 && ==

.&&0& =r P pr


8/13

=or > 12

;hus#

6. An oldgas turbinehas anefficienc% of21 percentanddevelops a

po eroutput of6000 kW.eterminethe fuel

.&--.8 ""6.&&

/"6.&&11.-.8 "

/11.1.&00&.8

/-.8 ""0.01-.1&

/&.81.*.&&0+

6

1

/"0.01&16.8*&86.1*+6+

1"

2&

"

&

"

21

22

&"

1

===

======

===

==

==

====

A

net

R Anet

R

A

r r

r r

Qw

kg kJ qq

kg kJ hh

kg kJ hh

kJ h P

P

P

kJ h P P P

pr ."8

/&-.-8/6.&80

/6.&80"1."0"&-.-8

/"1."0"1.&006.-0"

/&-.-860.610-.1&

/6.-0"8.2-*.&&0+

12

1

/6.6106&.16*&86.1*+12+

1"

2&

"

&

"

21

22

&"

1

===

======

===

====

====

kg kJ kg kJ

qw

kg kJ qqw

kg kJ hh

kg kJ hh

kkJ h P

P

P

kJ h P P P

A

net

R Anet

R

A

r r

r r

*+6.10.&-."8

+/."1"6.&&6.&80

increasee

increasekg kJ wnet ==

==


9/13

consumption rate of this gas turbine# in L/min# if the fuel has a heating valueof "2#000 k$/kg and a densit% of 0.8 g/cm&.

9olution:

-. 'onsider t o 'arnot heat engines operating in series. ;he first engine

receives heat from the reservoir at 1800 7 and re5ects the aste heat toanother reservoir at temperature T . ;he second engine receives this energ%re5ected b% the first one# converts some of it to ork# and re5ects the rest to areservoir at &00 7. !f the thermal efficiencies of both engines are the same#determine the temperature T .

9olution:

s L Lkg

skg mV

skg kg kJ skJ m

kJ skJ

eW

Q net A

/8 0.0/8.0

/680&.0

/680&.0/000#"2/-0#28

/-0#2821.0

/6000

===

==

===


10/13KKT

T T T

ThT T T

T

Th

T T

T e

Th

T e

h

*&00*+1800+

11

1

1

2

2

1

==

=

=

=


11/13

E

8. Air is used as the orking fluid in a simple ideal ?ra%ton c%cle that has a pressure ratio of 12# a compressor inlet temperature of &00 7# and a turbineinlet temperature of 1000 7. etermine the reFuired mass flo rate of air fora net po er output of -0 GW# assuming both the compressor and the turbinehave an isentropic efficienc% of + a* 100 percent and + b* 8 percent. Assumeconstant specific heats at room temperature.

9olution:

. An air standard c%cle ith variable specific heats is e)ecuted in a closeds%stem and is composed of the follo ing four processes:

1 2 v c!nstant heat addition from 1".- psia and803= in the amount of &00 ?tu/lbm2 & P c!nstant heat addition to &200 H & " !sentropic e)pansion to 1".- psia" 1 P c!nstant heat re5ection to initial state+a* 9ho the c%cle on P"v and T s diagrams.+b* 'alculate the total heat input per unit mass.


12/13

+c* etermine the thermal efficienc%

9olution:

10. ;he compression ratio of an ideal dual c%cle is 1". Air is at 100 k4a and&00 7 at the beginning of the compression process and at 2200 7 at the endof the heat addition process. eat transfer to air takes place partl% atconstant volume and partl% at constant pressure# and it amounts to 1 20."k$/kg. Assuming variable specific heats for air# determine + a* the fraction ofheat transferred at constant volume and + b* the thermal efficienc% of thec%cle.

9olution:


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problems on gas cycles in thermo

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