Question $1$:

A steam power plant operates on a Rankine cycle with a single open feedwater heater for

regeneration. The key parameters are as follows:

$$ Boiler pressure: $8$ MPa

$$ Boiler exit temperature: $480$C

$$ Condenser pressure: $10$ kPa

$$ Feedwater heater pressure: $1$ MPa

$$ Mass flow rate of steam: $20$ kg$/$s

In this cycle, steam expands isentropically in the turbine to the condenser pressure. A

portion of the steam is extracted at the feedwater heater pressure to preheat the feedwater

before it enters the boiler. The rest of the steam expands to the condenser pressure. Both

the feedwater pump and the main pump are assumed to operate isentropically$.$

Tasks:

$1.$ State Determination:

$$ Sketch the T$-$s diagram of the cycle, labeling all key states.

$$ Using steam property tables, determine the specific enthalpy $($h$)$ and entropy $($s$)$ at:

Boiler exit, turbine exit, condenser exit, pump exit, and feedwater heater extraction

point.

$2.$ Mass flow split:

$$ Determine the fraction of steam extracted for the feedwater heater $($yy$).$

$$ Calculate the mass flow rates in each branch of the cycle.

$3.$ Performance metrics:

$$ Calculate the following quantities:

$$ Work output of the turbine.

$$ Work input to the pump.

$$ Heat added in the boiler.

$$ Heat rejected in the condenser.

$$ Determine the overall thermal efficiency of the cycle.

$4.$ System discussion:

$$ Describe how regeneration improves thermal efficiency by reducing the energy

required to heat the feedwater and increasing the mean temperature of heat

addition.

$$ Discuss practical considerations of implementing regeneration, such as the trade$-$off

between efficiency gains and added system complexity.