Mathematics, Science, and Plant Calculations: Applying Formulas Under Exam Pressure
What this domain tests
This domain checks the arithmetic, algebra, and applied science used elsewhere on the exam: heat and energy balances, flow and pressure conversions, efficiency, and basic chemistry and physics. Items reward setting up the formula with consistent units before calculating.
Core rules and concepts
- Heat: Q = m x cp x temperature difference. Latent heat uses m x hfg with no temperature term.
- Efficiency: boiler efficiency = heat output / heat input x 100. Combustion efficiency from stack loss = 100 - stack loss.
- Pressure: 1 kPa = 0.145 psi; 1 bar = 100 kPa; gauge plus atmospheric equals absolute. Use absolute pressure in gas law calculations.
- Flow and energy: power = flow x head x density x gravity for pumps; electrical power = V x I x power factor x root-3 for three-phase.
- Gas laws: P1V1/T1 = P2V2/T2 with absolute temperature in kelvin (C + 273).
- Chemistry: pH is the negative log of hydrogen ion concentration; a drop of one pH unit is a tenfold increase in acidity.
Worked example
A boiler produces 5000 kg/h of steam with enthalpy rise of 2400 kJ/kg. Fuel input is 15 000 kW. What is the efficiency?
Reasoning: heat output = 5000 kg/h x 2400 kJ/kg = 12 000 000 kJ/h = 12 000 000/3600 kW = 3333 kW. Efficiency = 3333/15 000 x 100 = 22.2%. That is implausibly low for a boiler, so check the units: 5000 kg/h is 1.389 kg/s, and 1.389 x 2400 = 3333 kW, confirming the arithmetic. A result this low points to a data error, such as a mis-stated fuel input, not a real efficiency.
Traps that cost marks
- Mixing kg/h with kW without dividing by 3600.
- Using gauge pressure in the gas law instead of absolute.
- Forgetting to convert Celsius to kelvin.
- Reporting efficiency without checking that the answer is physically plausible.