This problem is an extension of **Problem
4.5** in which the Athenai Power Consulting
Group proposed a unique Cogeneration system for O'Bleness Hospital to
provide both 500kW electric power and hot water at 60°C. On analysis
we determined that the thermal efficiency η_{th}
of the proposed power plant was 23%, which is extremely low. In an
attempt to improve the plant thermal efficiency Athenai proposed a
new design as shown in the following schematic diagram:

The condenser hot water heating system is retained as
in the previous design with the hot water storage tank immersed in
the hotwell of the condenser. The turbine outlet pressure has been
reduced from the original 100 kPa to 20 kPa, and the steam condenses
to a subcooled hotwell temperature of 60°C, A condensate pump
increases the pressure to 200 kPa, allowing the air to separate and
escape in the Open Feedwater Heater/De-aerator. A mass fraction **y**
of saturated vapor steam at 200 kPa is tapped from the turbine and
mixed with the condensate as shown, and the resulting saturated
liquid mixture is then pumped to 4 MPa by the feedwater pump before
being supplied to the boiler. As a young engineer at Athenai your
purpose is to evaluate this new design and compare its performance to
the previously proposed system.

1) Neatly Plot the complete cycle on the

**P-h****(pressure-enthalpy)**diagram provided, indicating clearly stations (1), (2), (3), (4), (5), (6), and (7) on the diagram. Once this is done then use the**Steam Tables**to determine the following:2) Determine the mass fraction y of the bled steam at station (7) in order to provide a saturated liquid condition at station (5). [y = 0.103]

3) Determine the mass flow rate of the steam through the cycle required in order to provide the required turbine output power of 500kW. [0.554 kg/s]

4) Determine the overall thermal efficiency η

_{th}of this power plant. (Recall that thermal efficiency is defined as the net work done divided by the total heat supplied externally to the boiler. You may ignore the feedwater and condensate pump power in this evaluation. [32%]5) Compare the performance of the above system with that of the previously proposed system (

**Problem 4.5**), and discuss its advantages and disadvantages.

*Justify* all values used
and *derive* all
equations used starting from the basic energy equation for a flow
system, and the basic definition of thermal efficiency η_{th}.

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Engineering Thermodynamics by Israel
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