$8\mathrm{.}3$ Problems

Problem $1$: An idealized power plant operates according to the Rankine cycle with boiler and condenser pressures of $30$ bar and $0\mathrm{.}04$ bar $,$ respectively. The steam leaves the boiler in the superheated state at $350C$ and is then expanded in a turbine with an isentropic efficiency of $80\%.$ After expansion, the steam is fully condensed to form a saturated liquid. Subsequently, the saturated liquid is pumped with an isentropic efficiency of $85\%$ back to the boiler pressure to complete the cycle.

a$)$ Draw a block diagram and sketch a T$-$s diagram of the cycle.

b$)$ Calculate:

i$)$ The specific work input to the feed pump.

ii$)$ The heat input to the boiler.

iii$)$ The specific work output of the turbine.

iv$)$ The specific heat rejected in the condenser.

v$)$ The thermal efficiency of the plant.

vi$)$ The required water flow rate in the cycle if the plant produces $80$ MW of power.

c$)$ If heat is supplied from a reservoir at $400C$ and rejected to a reservoir at $20C,$ calculate:

i$)$ The entropy change in the two reservoirs.

ii$)$ The Second Law efficiency of the cycle using

a surroundings temperature of $20C$

Solution:$-$

B$)$

i$)-3\mathrm{.}539$ Kj

ii$)2991\mathrm{.}71$ KJ

iii$)867\mathrm{.}68$ kJ

iv$)-2127\mathrm{.}03$ KJ

v$)28\mathrm{.}9\%$

vi$)92\mathrm{.}58$ Kg

C$)$

i$)-4\mathrm{.}445$ Kj

ii$)51\mathrm{.}2\%$

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