properties of steam numericals v2
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Steam Tables
Steam tables provide properties of 1 kg of
dry and saturated steam for different
values of Pressure. (represented by bar)
If gauge pressure is given, it has to be
converted to absolute pressure by adding
atmospheric pressure to it
Abs Pr = Gauge Pr + Atm Pr
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Properties of steam: Numerical
Problem 1: Find the enthalpy of 1 kg of steam at
12 bar when,
(a) steam is dry saturated,
(b) steam is 22% wet and (c) superheated to 250C.
Assume the specific heat of the superheated
steam as 2.25 kJ/kgK
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(b) Enthalpy of Wet Steam :
When the steam is 22% wet, it will be 78% dry.
Therefore the dryness fraction x = 0.78hx = hf+x hfg
= 2346.18 kJ/kg
(c) Enthalpy of Superheated Steam:
hsup= hf+hfg+ Csup(Tsup- Tsat)
= 2922.23 kJ/kg
A
B C
Sensible
Heat
Latent
Heat
hfg
Tsup
Temperature
Enthalpy
Amount of
Superheat
Degree of Superheat
Ts
hf
D
Temperature
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Problem 2:Determine the conditions of steam from the
following data:
a) Pressure is 10 bar and temperature 200C,
b) Pressure is 12 bar and enthalpy of 2600 kJ/kg.
A
B C
Sensibl
e
Heat
Latent
Heat
hfg
Tsu
p
Temperatur
e
Enthalp
y
Amount of
Superheat
Degree of Superheat
Ts
hf
D
Temperatur
e
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Problem 3:Given enthalpy of steam at 30 bar is
3681 kJ. Is the steam wet or superheated? If it is
wet; find its dryness fraction. If it is superheated;find its degree of superheat.
Solution:From steam table, at 30 bar,
Tsat= 233.8C
hf
= 1008.3 kJ/kg.
hfg= 1794 kJ/kg.
hg= 2802.3 kJ/kg.
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Problem 4:By actual measurement, the enthalpy of
steam at 6 bar is found to be 2500 kJ/kg.
a) What is the quality of steam?b) If 500kJ/kg of heat is added to this steam, what
is the
Superheated temperature
Degree of superheat
Enthalpy of superheat
Solution: For 6 bar pressure,Tsat= 158.8
oC, hf= 670.4 kJ/kg,
hfg= 2085 kJ/kg, hg= 2755.5 kJ/kg.Dept. of Mech & Mfg. Engg.
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A
B C
Sensible
Heat
Latent
Heat
hfg
Tsup
Temperature
Enthalpy
Amount of
Superheat
Degree of Superheat
Ts
hf
D
Temperature
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Problem 5: 2 kg of water at 30oC is heated
continuously at constant pressure of 5 bar. The
total amount of heat added is 500 kJ. Determinethe dryness fraction or degree of superheat of the
resulting steam as the case may be.
Solution:
At 5 bar pressure, Tsat = 151.9oC, hf = 640.1 kJ/kg,
hfg= 2107.4 kJ/kg & hg= 2747.5 kJ/kg.
Initial enthalpy at 30o
C,hi = m. Cpw. T
= 2 x 4.1868 x 30
= 250.8 kJ for 2 kg of steam.
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But heat added is 500 kJ/kg.
Enthalpy after heat addition = 250.8 + 500
= 750.8 kJ { for 2 kg }Sensible heat for 2 kg = hfx 2
= 640.1 x 2 = 1280.2 kJ {for 2 kg}
Since enthalpy after heat addition [750.8] is lessthan that of enthalpy of saturated water
The resulting condition
after addition of heat is
unsaturated water.
A
B C
Sensible
Heat
Latent
Heat
hfg
Tsup
Temperature
Enthalpy
Amount of
Superheat
Degree of Superheat
Ts
hf
D
Temperature
hi
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Problem 6:2 boilers one with superheater
and another without superheater are
delivering equal quantities of steam into acommon main. The pressure in the boiler
and main is 20 bar. The temperature of
steam from the boiler with a superheater is350oC and the temperature of steam in the
main is 250oC. Determine the quality of
steam supplied by the other boiler.
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Solution:
Main, Steam flow
at 20 bar and
250oC
(superheated)
Steam flow from a
boiler [B1] with
superheater,
Pressure 20 bar
and 3500C
(Superheated)
Steam flow from a boiler
[B2]without superheater,
Pressure 20 bar,
(Unknown quality)
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Find the enthalpy of steam flowing from boilerB1 ie. P = 20 bar, T = 350oC,
From steam table at 20 bar,
Tsat= 212.4oC,
hf= 908.6 kJ/kg,
hfg= 1888.7 kJ/kghg= 2797.2 kJ/kg.
T > Tsat
, The steam is superheated.
hsup(B1) = hg+ Csup(Tsup- Tsat)
= 3106.8 kJ/kg ------ (1)
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Enthalpy of steam flowing in the main
pipe: i.e., at P = 20 bar, T = 250oC
T = 250oC > Tsat= 212.4 oC.The steam is superheated
hsup(Main) = hg + Csup(Tsup- Tsat)
= 2881.8 kJ/kg ------ (2)
For 2 kg = 2881.8 x 2 = 5763.6 kJ
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To find Enthalpy of steam flowing from B2:
We know that, at main, T = 250oC
at B1, T = 350oC,
So the steam flowing from Boiler with outsuperheater (B2) is wet
h = hf+ x.hfg= 908.6 + x(1888.7) ------ (3)
Energy balance, (2) = (1) + (3)
5763.6kJ = [3106.8]kJ + [908.6 + x(1888.7)]kJ
x = 92.56%
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Problem 7:1000 Kg of steam at a pressure
of 16 bar and 0.9 dry is generated by a
boiler per hour. Steam passes through asuperheater where its temperature is
raised such that the degree of superheat
is 180 oC. If the temperature of feed wateris 30 oC, determine
a) Total heat added to feed water per hour
to produce wet steam in the boiler.b) Total heat absorbed per hour in the
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Q: It is the point wherewet steam leaves theboiler with x = 0.9 andis the point wheresteam enters the
superheater.R: It is the point where itleaves the superheater.
A
B C
Sensible
Heat
Latent Heat
hfg
Tsup
Temperature
Enthalp
Amount of
Superheat
Degree of Superheat = 180
Ts=
201.4
hf
D
Temperature
p
q
r
Pressure =16 bar
At P = 16 bar,
Tsat= 201.4oC,hf= 858.5 kJ/kg
hfg=1933.2 kJ/kg
hg=2791.7 kJ/kg.
Solution:Solving per kg basis: i.e., m =1,
P: Entry of water into boiler
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Since, we know, Degree of superheat, Tsup- Tsat= 180oC
Tsup= 201.4 + 180 = 381.4oC
Answer to be calculated are:Heat supplied to feed water = hQhP
Heat absorbed in the superheater = hRhQ
hP= m.Cp.T
= 1 x 4.1868 x 30 = 125.4 kJ/kg.
hQ = hf+ x.hfg
= 858.5 + 0.9 x 1933.2 = 2598.38 kJ/kg.
hR= hg+ Csup(Tsup - Tsat)
= 2791.7 + 2.25(180) = 3196.7 kJ/kg.
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Heat supplied to feed water = hQhP
= 2472.98 kJ/kg.
For 1000 kg, heat supplied = 1000 x 2472.98
= 24,72,980 kJ.
Heat absorbed in the superheater = hRhQ= 598.32 kJ/kg.
For 1000 kg of steam,
heat absorbed = 1000 x 598.32= 5,98,320 kJ
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Problem 8:Feed water enters a boiler at 60oC at a
pressure of 15 bar. If it leaves the boiler at 0.9 dry
steam and leaves the superheater at 350o
C. Findthe heat supplied per kg of steam
a) in the Boiler and
b) In the superheater.
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Problem 9:
5 kg of water is heated from 40oC to superheated
steam at 150oC with constant pressure of 3 bar.Find,
a) The total amount of heat added in the heating
process, and
b) Amount of superheat
Solution :
From steam table, at 3 bar pressure,
Tsat= 133.5oC, hf= 561.4 kJ/kg, hfg= 2163.2 kJ/kg,
hg= 2724.7 kJ/kg.Dept. of Mech & Mfg. Engg.
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Initial condition is water at 40oC, i.e., at state-
point P on t-h diagram
Enthalpy at P= m.Cp.T
= 1 x 4.1868 x 40
= 167.2 kJ/kg.Enthalpy at q
= hg+ Csup(Tsup- Tsat)
= 2761.82 kJ/kg.A
B C
Sensible
Heat
Latent Heat
hfg
Tsup
Temperature
Enth
Amount of
Superheat
Degree of Superheat
Ts=
hf
D
Temperature
p
q
Pressure = 3 bar
40
Solving per kg basis:
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The amount of heat added in the heating process
= hq- hp
= 2594.62 kJ/kg.For 5 Kg, heat added = 5 x 2594.62
= 12973.125 kJ
Amount of superheat = Csup(Tsup- Tsat) x 5= 2.25(150133.5) x 5
= 185.625 kJ
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Problem 10:Feed water enters the boiler at
60oC at a pressure of 15 bar, it leaves the
boiler with 20% wet to enter a superheater,where it is superheated to 350oC. Find the
heat supplied per kg of steam,
In the boiler
In the superheater
Solution:
SensibleHeat
Amount of
Superheat
A
B C
Latent Heat
hfg
Tsup
Temperature
Enthalpy
Degree of Superheat
Ts=
hf
D
Temperature
p
q
Pressure = 15 bar
60
r
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Total heat supplied to feed water in the boiler =
hq-hp= 2538.7 kJ/kg
Total heat supplied in the superheater =hr-hq= 730.38 kJ/kg
SensibleHeat
Amount of
Superheat
A
B C
Latent Heat
hfg
Tsup
Temperature
Enthalpy
Degree of Superheat
Ts=
hf
D
Temperature
p
q
Pressure = 15 bar
60
r
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Problem 11:Dry saturated steam at a pressure of 16
bar is generated in a boiler. Dry saturated steam
leaves the boiler to enter a superheater, where itlooses heat equal to 600 kJ/kg. And in the
superheater, steam is superheated to
temperature of 380oC. If temperature of feed
water is 30oC, determine: Total heat supplied to feed water in the boiler
Dryness fraction of steam at the entry of
superheater
Total heat supplied in the superheater.
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At 16 bar pressure,
Tsat= 201.4oC,
hf= 858.5 kJ/kg,hfg= 1933.2 kJ/kg,
hg= 2791.7 kJ/kg.
Enthalpy at p= m.Cp.T
= 125.4 kJ/kg.
At q,ie. hg= 2791.7 kJ/kg. Sensible
HeatAmount of
Superheat
A
B C
Latent Heat
hfg
Tsup
Temperature
Enthalpy
Degree of Superheat
Ts=
hf
D
Temperature
p
q
Pressure = 16 bar
30
r
s
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Before it gets into superheater, it losses 600kJ/kg heat.
Enthalpy before it enters the superheater,hr= 2791.7 - 600 = 2191.7 kJ/kg.
Quality of steam before entering the
superheater, hr = hf+ x.hfg2191.7 = 858.5 + x .1933.2
x = 0.6896
Enthalpy of superheated steam coming outfrom superheater,
hs= hg+ Csup(Tsup- Tsat)
= 3193.55 kJ/kg.Dept. of Mech & Mfg. Engg.
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Total heat supplied to feed water in the
boiler = hq- hp = 2666.33 KJ/Kg.
Dryness fraction of steam beforeentering superheater = 68.96%
Total heat supplied in the superheater
= hshr = 1001.85 KJ/Kg
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Problem 12: The steam initially at a pressure
of 9bar and dryness 0.98. Find the final quality
and temperature of steam at each of thefollowing operations.
A) When steam loses 50 KJ/Kg at constant
pressure
B) When steam receives 150 KJ/Kg atconstant pressure
Solution: At P = 9bar, Tsat= 175.4
oC, hf = 742.6 KJ/kg, hfg=
2029.5 KJ/kg, hg = 2772.1 KJ/kg,
given x1= 0.98
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Steam is superheated. To find Tsup., hs= hg + Csup(Tsup- Tsat)
2881.5 = 2772.1 + 2.25 (Tsup175.4)
Tsup = 223.6oC
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Problem 13: The steam initially at a pressure
of 9bar and 98% dry expands in a turbine such
that it losses 80 KJ/kg at a constant pressure.a) What is the quality of steam after
expansion?
B) If it receives 160 KJ/kg heat before
expansion, what would be the final state andtemperature of the steam?
Solution:
Answer a) x = 94 %b) T sup = 192.9
oC
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