Question

A steam power plant uses steam as working fluid and operates at a boiler pressure of 5 MPa,

dry saturated and a condenser pressure of 5 kPa. Determine the cycle efficiency for (a) Carnot

cycle (b) Rankine cycle. Also show the T-s representation for both the cycles​

Answer 1

Answer: Rankine 36.56 %

Explanation:

At 5 MPa

At 5 kPa

hy SMP1154.23 kJ/kg, 8.5 MPa = 2 he, 5MPa 2794.3 kJ/kg, 8g. 5 MPa = 5.!

hy, 5kPa 137.82 kJ/kg, 8.5kPa = 0.47

hg, kPa = 2561.5kJ/kg, 8,5 = 8.39

. 5kPa = 0.001005 m³/kg As process 2-3 is isentropic, so 82 83

Carnot cycle: 1-2-3-4-1 Rankine cycle: 1-2-3-5-6

83 = 87, SkPa +23 8/g. 5kPa = 82 = 8.5MPa

Hence enthalpy at 3,

23 0.694

Enthalpy at 2,

h3=hy skPa+23: hig. 5kPa hs 1819.85 kJ/kg

hgh SMP 2794.3 kJ/kg

Process 1-4 is isentropic, so

8184 82.92 0.4764+ (8.3951-0.4764)

Rothalat at

24= 0.308

Enthalpy at 4,

ha=137.82+ (0.308 (25 h=884.3 kJ/kg

(2561.5-137.82))

Enthalpy at 1,

h₁ = hy at 5 MPa

Carnot cycle

h = 1154.23 kJ/kg

Пcarnot

Net work

Heat added

(ha ha)-(h-ha) (h₂-hi)

{(2794.3-1819.85)-(1154.23-884.3)}

(2794.3 1154.23)

or

carnot 0.4295

In Rankine cycle, 1-2-3-5-6-1

carnot 42.95 %

Pump work, he hs v5(P6-Ps)

: -0.001005(5000-5)

he hs 5.02

hs=hy at 5kPa = 137.82 kJ/kg Hence he 137.82+5.02 142.84 kJ/kg

he 142.84 kJ/kg

Net work in Rankine cycle= (h2-hs) - (he-hs)

-974.45-5.02

969.43 kJ/kg

Heat added h₂-he

=2794.3-142.84

=2651.46 kJ/kg

Rankine cycle efficiency = 969.43 2651.46

or

Rankine 0.3656

Rankine 36.56 %

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