(a) A cogenerating steam power plant operates with a boiler output of 25 kg/s steam at 7 MPa, 500°C. The condenser operates at…

(a)(i) At 7.5 kPa, saturated liquid has T_sat = 40.3°C and v_f = 0.001008 m³/kg. The condenser pump raises the condensate to the process-return/mixing pressure of 100 kPa. For an ideal pump with incompressible liquid, w_p = v_f(100 − 7.5) kPa = 0.001008 × 92.5 = 0.0932 kJ/kg. Temperature rise = w_p/c_p = 0.0932/4.187 = 0.022 K. Therefore, T leaving condenser pump = 40.3 + 0.022 = 40.32°C ≈ 40.3°C. Condition: ideal pump, negligible kinetic and potential energy changes.

(a)(ii) At turbine inlet: h₁ = 3410 kJ/kg, s₁ = 6.802 kJ/kg K. At 500 kPa: s_f = 1.8607, s_g = 6.8213, h_f = 640.2, h_fg = 2108.5 kJ/kg. x₂ = (6.802 − 1.8607)/(6.8213 − 1.8607) = 0.9961. h₂ = 640.2 + 0.9961 × 2108.5 = 2740.5 kJ/kg.

At 7.5 kPa: s_f = 0.5764, s_g = 8.2515, h_f = 168.8, h_fg = 2405.8 kJ/kg. x₃ = (6.802 − 0.5764)/(8.2515 − 0.5764) = 0.8111. h₃ = 168.8 + 0.8111 × 2405.8 = 2120.3 kJ/kg.

Total turbine output: W_T = 25(3410 − 2740.5) + 20(2740.5 − 2120.3) = 25 × 669.5 + 20 × 620.2 = 16737.5 + 12404 = 29141.5 kW. W_T ≈ 29.14 MW.

(a)(iii) Process steam leaves as saturated liquid at 100 kPa, where h_f = 417.5 kJ/kg. Q_process = 5(2740.5 − 417.5) = 5 × 2323 = 11615 kW. Q_process ≈ 11.62 MW.

(b) Basis: 1 kg fuel. C = 0.85 kg → 0.85/12 = 0.07083 kmol C H = 0.10 kg → 0.10/1 = 0.10 kmol H atoms O = 0.03 kg → 0.03/32 = 0.0009375 kmol O₂ equivalent N = 0.02 kg → 0.02/28 = 0.000714 kmol N₂

Stoichiometric O₂ required: n_O₂,st = C + H/4 − O₂ equivalent = 0.07083 + 0.10/4 − 0.0009375 = 0.09490 kmol O₂/kg fuel.

Mass O₂ required = 0.09490 × 32 = 3.037 kg. Taking air as 21% O₂ and 79% N₂ by volume, air mass required = 3.037/0.233 = 13.03 kg/kg fuel. Chemically correct A/F ratio = 13.03 : 1.

With 30% excess air: n_O₂,supplied = 1.3 × 0.09490 = 0.12336 kmol. n_N₂ from air = 0.12336 × (79/21) = 0.46409 kmol. Total N₂ = 0.46409 + 0.000714 = 0.46480 kmol. CO₂ formed = 0.07083 kmol. Excess O₂ = 0.12336 − 0.09490 = 0.02847 kmol. H₂O formed = 0.10/2 = 0.05 kmol (not in dry products).

Dry product masses: m_CO₂ = 0.07083 × 44 = 3.117 kg m_O₂ = 0.02847 × 32 = 0.911 kg m_N₂ = 0.46480 × 28 = 13.014 kg Total dry mass = 17.042 kg.

By weight: CO₂ = 3.117/17.042 × 100 = 18.29% O₂ = 0.911/17.042 × 100 = 5.35% N₂ = 13.014/17.042 × 100 = 76.36%

Dry moles: n_CO₂ = 0.07083, n_O₂ = 0.02847, n_N₂ = 0.46480. Total = 0.56410 kmol.

By volume: CO₂ = 0.07083/0.56410 × 100 = 12.56% O₂ = 0.02847/0.56410 × 100 = 5.05% N₂ = 0.46480/0.56410 × 100 = 82.39%

(c) In SI engines, knock is autoignition of the unburnt end gas. Molecular structure controls self-ignition temperature and pre-flame reaction rate. Straight-chain paraffins form peroxides readily and autoignite early, so they knock strongly and have low octane number; knock increases with chain length. Branching and compact iso-paraffins hinder peroxide formation, giving high octane and low knock. Olefins are more knock-resistant than corresponding paraffins but less than aromatics. Aromatics have stable ring structures, high self-ignition temperatures and hence least knock; naphthenes are intermediate, better than straight-chain paraffins but worse than aromatics. In CI engines the requirement reverses: long straight-chain paraffins have high cetane number, ignite readily and reduce diesel knock, while aromatics have low cetane number and increase diesel knock.