Problem Statement

A steam power plant uses water as the working fluid and operates on the ideal Rankine cycle.

Liquid water at $0\mathrm{.}70$ bar is compressed in a pump isentropically to a pressure of $50$ bar. The

isentropic efficiency of the pump is $92\%.$ The water is then heated, first in a boiler, and then

superheated in a superheater to $400C.$ The pressure loss in the boiler and superheater is

negligible. Approximately $20$ MW of power is generated by the turbine. The turbine has an

isentropic efficiency of $87\%.$ In the condenser, cooling water is used to condense the exhaust steam

from the turbine to a saturated liquid. The temperature rise of the cooling water is $15C.$ The

pressure loss in the condenser is negligible.

$($a$)$ Sketch a block diagram of the cycle.

$($the processes are to be numbered as: boiler $4-1$; turbine $1-2$; Condenser $2-3$; Pump $3-4)$

$($b$)$ Sketch the cycle on a T$-$s diagram.

$($c$)$ Determine the cycle efficiency and the work ratio.

$($d$)$ Determine the mass flow rate of the steam, in $k\frac{g}{s}.$

$($e$)$ Determine the mass flow rate of the cooling water, in $k\frac{g}{s}.$

The specific heat capacity of the cooling water is $4\mathrm{.}18k\frac{J}{k}g.C.$

Note: You are not required to interpolate values in the Steam Tables, use the closest corresponding

values.