In a steam power plant operating on a ideal Rankine cycle,

Home » Thermodynamics » Thermodynamics Miscellaneous » Question

In a steam power plant operating on a ideal Rankine cycle, superheated steam enters the turbine at 3 MPa and 350°C. The condenser pressure is 75 kPa. The thermal efficiency of the cycle is ________%. Given data: For saturated liquid, at p = 75 kPa, hf = 384.39 kJ/kg, v_f = 0.001037 m³/kg, s_f = 1.213 kJ/kgK. At 75 kPa, h_fg = 2278.6 kJ/kg, s_fg = 6.2434 kJ/kgK At P = 3 MPa and T = 350°C (superheated steam), h = 3115.3 kJ/kg, s = 6.7428 kJ/kgK.

1. 0.26 or 26%
2. 0.25 or 25%
3. 0.27 or 27%
4. 0.36 or 36%

Correct Option: A

h₁ = 3115.3 kJ/kg
s₁ = 6.7428 kJ/kg
s₁ = s₂ = s_f + xs_fg

x =		6.7428 - 1.213	=	5.5298	= 0.8857
		6.2434		6.2434

h₂ = h_f + xh_fg
= 348.39 + 0.8857 × 2278.6
= 348.39 + 2018.16
= 2402.55 kJ/kg
Pump work = W_p = v_f (p₄ – p₃) = 3.033 kJ/kg
h₄ = h₃ + v_f (p₄ – p₃)
= 384.34 + 0.001037(3000 – 75)
= 384.34 + 3.033 = 387.37 kJ/kg
W_net = W_T – W_P = (h₁ – h₂) – W_P
= (3115.3 – 2402.55) – 3.033
= 709.72 kJ/kg
Q_s = heat supplied = h₁ – h₄
= 3115.3 – 387.37
= 2727.93 kJ/kg

η_th =	W_net
	Q_s

=	709.72	× 100 = 0.26 or 26%
	2727.93