FME 421: THERMODYNAMICS IV TUTORIAL
1. A Carnot steam cycle operates between a source temperature of 317 ℃ and a sink
temperature of 17 ℃. Determine the thermal efficiency and the ratio of turbine work to
compressor work, when;
a) All the processes are reversible
b) The isentropic efficiency of the turbine is 0.80 and that of the compressor is 0.60.
2. The turbine of a Rankine steam cycle operates with saturated vapor at a temperature of 317
℃ and the exhaust steam is at a temperature of 17 ℃. Determine the thermal efficiency and
the ratio of turbine work to pump work, when;
a) All the processes are reversible
b) The isentropic efficiency of the turbine is 0.80 and that of the pump is 0.96.
3. In a reversible Rankine cycle with superheat, steam enters the turbine at 17 bar and 427 ℃
and exhausts at 0.07 bar.
a) Find the network per kg of steam
b) If the isentropic efficiency of the turbine is 0.85, find the resulting network per kg of
steam
4. The high pressure turbine of a Rankine steam cycle with a reheat system is supplied with
steam at 80 bar and 450 ℃ where it is expanded to 20 bar. It is then reheated to 425 ℃ after
which it expands in the low pressure turbine to 0.08 bar.
a) What is the thermal efficiency?
b) How does this efficiency compare with that of Rankine cycle where the steam
expand from 80 bar and 450 ℃, without reheat, to 0.08 bar?
5. In a regenerative Rankine cycle with a condenser pressure of 10 kPa, steam enters the highpressure turbine at 16 MPa and 600 ℃. Some steam is extracted from the high-pressure
turbine at 5 MPa and sent to the first regenerative chamber; the remaining steam is reheated
to 600 ℃, and then expanded in the lower-pressure turbine to the condenser pressure, but
some steam is extracted from the lower-pressure turbine at 1 Mpa and sent to the second
regenerative chamber. Assuming that both regenerative chambers are open feedwater
heaters, and the liquid leaving the chambers is saturated liquid, determine
a) The steam fraction extracted from the turbines
b) The thermal efficiency of the cycle.
6. An ideal Rankine steam reheat cycle is utilized in power plant where the steam enters the
high-pressure turbine at 50 bar, 450 °C, and then expands to a dry saturated vapor state. The
exhaust steam from the high-pressure turbine is then reheated to 400 °C and expands to
0.075 bar in the low-pressure turbine. If the required pump power is 240.3 kW and the
exhaust steam from the low-pressure turbine leaves the condenser as saturated liquid,
determine:
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i.
ii.
iii.
iv.
v.
The steam mass flow rate,
The exit pressure from the high-pressure turbine,
The net power output.
The cycle thermal efficiency
the cycle work ratio.
7. A steam power plant equipped with a regenerative-reheat arrangement is supplied with
steam to the H.P turbine at 60 bar and 500 ºC where the steam is expanded to a pressure of 8
bar. Regeneration is effected by extracting a part of the exhaust steam leaving the H.P
turbine at 8 bar and the remainder of the steam is reheated to 450 ºC in a reheater and then
expanded in the L.P turbine down to 0.1 bar. Taking the isentropic efficiencies of the H.P
and L.P turbines to be 0.85, determine:
(i)
Amount of steam bled-off feed heating
(ii)
The net power output
(iii)
Thermal cycle efficiency
(iv)
Specific steam consumption
The steam supplied by the boiler is 3450 kg/hour.
8. A two stage velocity compounded impulse steam turbine has mean blade speed of 150 m/s;
steam leaves nozzle with 680 m/s velocity at angle of 20º. The exit angles of first row
moving blades, fixed blades, and second row moving blades are 25º, 25º, and 32º,
respectively. If all the blades have a blade velocity coefficient of 0.9; for a steam flow rate
of 5.5 kg/s, determine:
i.
ii.
iii.
9. (a)
The power output,
The specific steam consumption,
The diagram efficiency.
Prove that the maximum discharge of fluid per unit area through a nozzle occurs
 n 


 2  n - 1 
when the ratio of fluid pressure at the throat to the inlet pressure is, 
,

 n  1
where n is the index of adiabatic expansion.
(b)
A convergent-divergent nozzle operates with 5 kg of steam per minute being
discharged at 1 bar. If the steam is supplied to the nozzle at 8 bar and 250 ºC, for
supersaturating expansion upto the throat then normal expansion, determine;
i.
the steam state at the throat,
ii.
the temperature at the throat,
iii.
the throat area, neglect the inlet velocity to the nozzle.
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For supersaturation take pv1.3 = constant and
P
1.3
 constant .
T 0.3
10. A convergent-divergent nozzle is fed with steam at 9 bar, 350 ºC and expands isentropically
to 0.4 bar. Neglecting initial velocity at entry, calculate :
(a)
the exit area required for a mass flow rate of 0.25 kg/s for equilibrium and
supersaturated flow
(b)
the degree of supercooling and the degree of supersaturation.
For supersaturated and superheated regions assume pv1.25 = constant.
11. (a)
Briefly discuss the comparisons between the Carnot and the theoretical single stage
vapour compression refrigeration cycles.
(b)
A vapour compression cycle works on Ammonia-717 refrigerant with condensation
temperature of 34ºC and evaporator temperature of -20ºC. Refrigeration effect of 8.58 tons
is desired from the cycle. The compressor runs with 850 rpm and has a clearance of 4%.
Considering compression index of 1.13 determine;
i.
the refrigerating effect
ii. the COP
iii. the piston displacement in the reciprocating compressor used for compression.
Take 1 ton of refrigeration to be equivalent to 3.5 kW.
Assume no pressure drop and heating of the suction vapour
12. (a)
List five desirable characteristics of a refrigerant.
(b)
Ammonia is used as a refrigerant in a vapor-compression refrigeration system. The
condensing temperature is 35 ºC while the evaporating temperature is -20 ºC. The refrigerant
enters the compressor dry saturated and leaves the condenser as saturated liquid. For this
system, determine;
(i).
net work
ii.
Refrigeration effect
iii.
Loss of work due to throttling
iv.
Refrigeration efficiency.
Assume an isentropic process in the compressor.
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