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98 Brett Road
•
Piscataway
•
NJ 088548058
•
Phone: (732) 4453655
FAX: (732) 4450730
•
email: muller@caes.rutgers.edu
Center for Advanced Energy Systems
Michael R. Muller, Director
Problem Set: Thermodynamics Review  Steam
1.
An adiabatic pistoncylinder system contains a 1000W immersion heater and 4 kg of H
2
0 initially at
1 atm and 96 percent quality. The heater is operated for
7
min., during which the pressure is held
constant. Find the final volume of the system.
Solution:
Process is constant pressure. It is a control mass problem. Recall with control
mass you can determine changes in internal energy and work separately.
Normally this is the simplest way if you have the final conditions.
In this problem you are only told that it is a constant pressure process. For this
case, the heat input is equal to the change in enthalpy which fixes the final
state.
M
Q
h
h
Q
H
H
V
V
P
Q
U
U
PdV
Q
dW
dQ
dE
initial
final
initial
final
initial
final
initial
final
/
)
(
=
−
=
−
−
−
=
−
−
=
+
=
δ
Find the energy added by heat transfer into the system by the immersion heater (a
Watt is a joule/sec). The energy added is 420 kJ or 105 kJ/kg
The original state is fixed by the pressure and quality of the steam:
The original enthalpy  2585.71 kJ/kg
The original specific volume is – 1.61 m
3
/kg
The original volume is  6.44 m
3
Get the second enthalpy by using the first law:
New enthalpy – 2690.71 kJ/kg (just add the heat in)
Final specific volume – 1.72 m
3
/kg
Final volume = 4 kg * 1.72 m
3
/kg = 6.88 m
3
Note, even though you equated enthalpy change with heat transfer to solve this
problem, there is work done.
Determine the amount of work out of the system:
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2
Michael R. Muller, Director
W = P(V
final
– V
initial
) = 100000 N/m
2
x (0.44)
or 44 kJ
And the internal energy change can then be determined from the first law
2.
Steam flows through a small steam turbine at the rate of 10,000 kg/h, entering at 600
0
C and 2.0 MPa
and emerging at 0.01 MPa with 4 percent moisture. The flow enters at 50 m/s at a point 2 m above the
discharge and leaves at 80 m/s. Compute the shaftpower output, assuming that the device is adiabatic
but considering kinetic and potential energies. How much error would be made were these secondary
terms neglected? What are the areas of the inlet and discharge pipes?
Solution:
Note – 4% moisture is the same as a quality of 96%
Find inlet states:
h = 3690 kJ/kg
v = 0.1996 m
3
/kg
mass flow rate = 10000 kg/h yields volume flow rate = 1996 m
3
/hr. With
velocity of 50 m/s obtain
inlet area = 0.011 m
2
Find outlet states:
h = 2489 kJ/kg
v = 14.09 m
3
/kg
mass flow rate = 10000 kg/h yields volume flow rate = 140,900 m
3
/hr. With
velocity of 80 m/s obtain
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 Fall '10
 Muller

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