Test
8.3 Water is the working fluid in a Carnot vapor power cycle. Saturated liquid enters the boiler at a
pressure of 10 MPa, and saturated vapor enters the turbine. The condenser pressure is 6 kPa. Determine
(a) The thermal efficiency.
(b) The back work ratio.
(c) The heat transfer to the working fluid per unit mass passing through the boiler, in kJ/kg.
(d) The heat transfer from the working fluid per unit mass passing through the condenser, in kJ/kg.
8.10 Water is the working fluid in an ideal Rankine cycle. The pressure and temperature at the turbine
inlet are 1400 lbf/in2 and 1100 °F, respectively, and the condenser pressure is 2 lbf/in2. The mass flow
rate of steam entering the turbine is 1* 109 lb/h. The cooling water experiences a temperature increase
from 60 to 76°F, with negligible pressure drop, as it passes through the condenser. Determine for the
cycle
(a) The mass flow rate of steam, in lb/h
(b) The rate of heat transfer, in Btu/h, to the working fluid passing through the steam generator
(c) The thermal efficiency,
(d) The mass flow rate of cooling water, in lb/h.
8.13 Figure P8.13 provides steady-state operating data for a solar power plant operating on a Rankine
cycle. Refrigerant 134a is the working fluid. The turbine and pump work adiabatically.. The rate of
energy input to the collectors from solar radiation is 0.3 kW per m2 of collector surface area, with 60%
of the solar input to collectors absorbed by the refrigerant as it passes through the collector. Determine
the minimum possible solar collector surface area, in m2 per kW of power developed by the plant.
Discuss possible operational improvements that could reduce the required collector surface area.
8.17 Water is the working fluid in a Rankine cycle. Superheated vapor enters the turbine at 10 MPa,
480°C and the condenser pressure is 6 kPa. The turbine and pump have isentropic efficiencies of 80
and 70%, respectively. Determine for the cycle
(a) The rate of heat transfer to the working fluid passing through the steam generator, in kJ per kg of
steam flowing.
(b) The thermal efficiency.
(c) The rate of heat transfer from the working fluid passing through the condenser to the cooling water,
in kJ per kg of steam flowing.
8.25 Superheated steam at 18 MPa, 560 °C enters the turbine of a vapor power plant. The pressure at
the exit of the turbine is 0.06 bar, and liquid leaves the condenser at 0.045 bar, 26 °C The pressure is
increased to 18.2 MPa across the pump. The turbine and pump have isentropic efficiencies of 82 and
77%, respectively. For the cycle, determine
(a) The net-work per unit mass of steam flow, in kJ/kg.
(b) The heat transfer to steam passing through the boiler, in kJ per kg of steam flowing.
(c) The thermal efficiency.
(d) The heat transfer to cooling water passing through the condenser, in kJ per kg of steam condensed.
8.32 An ideal Rankine cycle with reheat uses water as the working fluid. The conditions at the inlet to
the first-stage turbine are p1 = 2500 lbf/in2, T1 = 1000°F. The steam is reheated at constant pressure p
between the turbine stages to 1000 °F. The condenser pressure is 1 lbf/in2.
(a) If p/p1 = 0.2, determine the cycle thermal efficiency and the steam quality at the exit of the secondstage turbine.
(b) Plot the quantities of part (a) versus the pressure ratio p/p1 ranging from 0.05 to 1.0.
8.37 Water is the working fluid in an ideal regenerative Rankine cycle. Superheated vapor enters the
turbine at 10 MPa, 480°C and the condenser pressure is 6 kPa. Steam expands through the first-stage
turbine to 0.7 MPa where some of the steam is extracted and diverted to an open feed water heater
operating at 0.7 MPa. The remaining steam expands through the second-stage turbine to the condenser
pressure of 6 kPa. Saturated liquid exits the feed water heater at 0.7 MPa. Determine for the cycle
(a) The rate of heat addition, in kJ per kg of steam entering the first-stage turbine.
(b) The thermal efficiency.
(c) The rate of heat transfer from the working fluid passing through the condenser to the cooling water,
in kJ per kg of steam entering the first-stage turbine.
8.69 Consider a regenerative vapor power cycle with two feedwater heaters, a closed one and an open
one, and reheat. Steam enters the first turbine stage at 12 MPa, 480 °C and expands to 2 MPa. Some
steam is extracted at 2 MPa and fed to the closed feedwater heater. The remainder is reheated at 2 MPa
to 440 °C and then expands through the second-stage turbine to 0.3 MPa, where an additional amount
is extracted and fed into the open feedwater heater operating at 0.3 MPa. The steam expanding through
the third-stage turbine exits at the condenser pressure of 6 kPa. Feedwater leaves the closed heater at
210 °C, 12 MPa, and condensate exiting as saturated liquid at 2 MPa is trapped into the open feedwater
heater. Saturated liquid at 0.3 MPa leaves the open feedwater heater. Assume all pumps and turbine
stages operate isentropically. Determine for the cycle
(a) The rate of heat transfer to the working fluid passing through the steam generator, in kJ per kg of
steam entering the first-stage turbine.
(b) The thermal efficiency.
(c) The rate of heat transfer from the working fluid passing through the condenser to the cooling water,
in kJ per kg of steam entering the first-stage turbine.
8.76 A binary vapor power cycle consists of two ideal Rankine cycles with steam and ammonia as the
working fluids. In the steam cycle, superheated vapor enters the turbine at 6 MPa, 640 °C and saturated
liquid exits the condenser at 60°C. The heat rejected from the steam cycle is provided to the ammonia
cycle, producing saturated vapor at 50 °C, which enters the ammonia turbine. Saturated liquid leaves
the ammonia condenser at 1 MPa. For a net power output of 20 MW from the binary cycle, determine
(a) The power output of the steam and ammonia turbines, respectively, in MW.
(b) The rate of heat addition to the binary cycle, in MW.
(c) The thermal efficiency.
8.78 Figure P8.78 shows a vapor power cycle with reheat and regeneration. The steam generator
produces vapor at 1000 lbf/in2, 800 °F. Some of this steam expands through the first turbine stage to
100 lbf/in2 and the remainder is directed to the heat exchanger. The steam exiting the first turbine stage
enters the flash chamber. Saturated vapor and saturated liquid at 100 lbf/in2 exit the flash chamber as
separate streams. The vapor is reheated in the heat exchanger to 530°F before entering the second
turbine stage. The open feedwater heater operates at 100 lbf/in2 and the condenser pressure is 1 lbf/in2
each turbine stage has an isentropic efficiency of 88% and the pumps operate isentropically. For a net
power output of 5 * 109 Btu/h determine
(a) The mass flow rate through the steam generator, in lb/h.
(b) The thermal efficiency of the cycle.
(c) The rate of heat transfer to the cooling water passing through the condenser, in Btu/h.