(a) A two-stage turbine receives steam at 50 bar and 350 °C. At 1·5 bar, the high-pressure stage exhausts and 12000 kg of steam…

(a)

State 1 (Inlet): 50 bar, 350 °C. Given: h₁ = 3068.4 kJ/kg, s₁ = 6.4492 kJ/kg-K.

HP Stage (1 → 2): The steam expands to 1.5 bar. For an isentropic expansion, s₂s = s₁ = 6.4492 kJ/kg-K. From steam tables at 1.5 bar: s_f = 1.4337, s_fg = 5.7897. Quality x₂s = (6.4492 - 1.4337) / 5.7897 = 0.866. Enthalpy h₂s = h_f + x₂s · h_fg = 467.11 + (0.866 × 2226.5) = 2395.2 kJ/kg. Isentropic work wₛ,HP = 3068.4 - 2395.2 = 673.2 kJ/kg. Actual work w_HP = η_HP × wₛ,HP = 0.84 × 673.2 = 565.5 kJ/kg. Actual exhaust enthalpy h₂ = 3068.4 - 565.5 = 2502.9 kJ/kg.

LP Stage (3 → 4): The remaining steam is reheated to 250 °C at 1.5 bar. Given: h₃ = 2972.65 kJ/kg, s₃ = 7.8709 kJ/kg-K. Expansion to 0.05 bar. Isentropic s₄s = 7.8709 kJ/kg-K. At 0.05 bar: s_f = 0.4762, s_fg = 7.9187. Quality x₄s = (7.8709 - 0.4762) / 7.9187 = 0.9338. Enthalpy h₄s = 137.75 + (0.9338 × 2423.7) = 2401.0 kJ/kg. Isentropic work wₛ,LP = 2972.65 - 2401.0 = 571.65 kJ/kg. Actual work w_LP = 0.81 × 571.65 = 463.0 kJ/kg.

Total Power Balance: Let m be the total steam rate (kg/h). Power = (Mass flow to HP × w_HP + Mass flow to LP × w_LP) / 3600. 3750 = [ (m × 565.5) + ((m - 12000) × 463.0) ] / 3600. 13,500,000 = 565.5m + 463.0m - 5,556,000. 19,056,000 = 1028.5m. m = 18,528 kg/h.

Conclusion: The rate of steam generated by the boiler is 18,528 kg/h.

(b)(i)

Effective temperature is the temperature of still, saturated air that would produce the same thermal sensation as the actual air conditions. It accounts for the combined effects of dry-bulb temperature, humidity, air velocity, and radiation.

Factors affecting optimum effective temperature:

1. Humidity: High humidity reduces the body's ability to cool via evaporation, requiring a lower effective temperature for comfort.
2. Air Velocity: Increased air speed enhances convective and evaporative heat loss, allowing for a higher effective temperature.
3. Radiation: High radiant heat from walls or the sun increases the thermal load, necessitating a lower effective temperature.
4. Activity (metabolic rate): Higher physical activity generates more internal heat, shifting the optimum lower.
5. Clothing: heavier winter clothing lowers the optimum ET; light summer clothing raises it.
6. Climate and season: people acclimatised to hot climates prefer a higher ET; the optimum is higher in summer than in winter.
7. Age and sex: older people and women generally prefer an ET about 0.5–1 °C higher.
8. Duration of stay: for short stays (shops, banks) the optimum is kept closer to outdoor conditions to avoid thermal shock; for long stays (offices, homes) a lower, steadier ET is chosen.
9. Density of occupants: crowded spaces need a lower ET because of body heat and moisture. The usual comfort range is about 21–23 °C ET in winter and 22–25 °C ET in summer.

(b)(ii)

Adiabatic mixing is a psychrometric process where two air streams at different states are mixed without any heat exchange with the surroundings.

Process Characteristics:

1. Conservation of Mass: The total mass of dry air in the mixture is the sum of the dry air masses of the individual streams (m₁ + m₂ = m₃).
2. Conservation of Energy: The total enthalpy of the mixture equals the sum of the enthalpies of the incoming streams (m₁ h₁ + m₂ h₂ = m₃ h₃).
3. Humidity Ratio: The humidity ratio of the mixture is the weighted average of the individual humidity ratios.

Chart Representation: On a psychrometric chart, the state of the mixture (Point 3) lies on the straight line connecting the initial states (Points 1 and 2). The position of Point 3 is determined by the mass ratio of the two streams.

From the two balances, (h₃ − h₁)/(h₂ − h₃) = (W₃ − W₁)/(W₂ − W₃) = m₂/m₁, so point 3 divides line 1–2 in the inverse ratio of the masses (nearer the larger stream). The dry-bulb temperature of the mixture is only approximately the mass-weighted average. If the line 1–2 crosses the saturation curve (mixing very cold and very humid air), condensation occurs and fog forms. In air-conditioning, this process is used to blend recirculated air with fresh outdoor air.

(c)

Necessity of Cooling: Internal combustion engines must be cooled because a significant portion of the heat generated by fuel combustion (approximately 30%) is not converted into mechanical work. If this heat is not removed, the engine temperature would rise to a point where metal components lose their strength, lubricating oil would break down (coking), and the engine would suffer catastrophic failure.

Disadvantages of Overcooling:

1. Reduced Efficiency: More heat flows from the working gases to the cold cylinder walls, so less of the fuel energy is converted into work and thermal efficiency falls.
2. Increased Friction: Overcooling increases the viscosity of the engine oil, which increases internal friction and power loss.
3. Poor Combustion: A cold engine leads to incomplete combustion and a rich fuel mixture, resulting in higher fuel consumption and increased emissions.
4. Corrosion: Overcooling can cause condensation of water and acids inside the engine, leading to internal corrosion.
5. Wear and sludge: Unburnt fuel washes oil off the cylinder walls and dilutes the crankcase oil; condensed water forms sludge, increasing wear of rings and liners.
6. Hard starting and poor vaporisation of fuel in SI engines; longer ignition delay and diesel knock in CI engines.