Engineering Mathematics, Thermodynamics and Applied Mechanics
Core concepts
Revise basic algebra, ratios, percentages, and unit conversion. Understand the gas laws, the first law of thermodynamics, sensible and latent heat, and the Carnot and real cycle efficiency. Know mechanics: force, moment, work, power, stress, strain, and the meaning of Young's modulus. Be able to read and use simple graphs and tables.
Traps in questions
- Mixing absolute and gauge pressure; the gas laws need absolute pressure.
- Using degrees Celsius in gas law calculations instead of kelvin.
- Confusing work and power; power is work per unit time.
- Forgetting that efficiency is always less than one and is often expressed as a percentage.
Rule of thumb and worked example
Gas law: P1V1/T1 = P2V2/T2 with absolute values. If 2 m³ of air at 300 K and 100 kPa is compressed to 0.5 m³ at 400 K, then P2 = P1 × (V1/V2) × (T2/T1) = 100 × (2/0.5) × (400/300) = 100 × 4 × 1.333 = 533 kPa absolute. Subtract atmospheric pressure if gauge pressure is asked. Always state whether the answer is absolute or gauge.
Study focus
Revise thermal efficiency of a diesel cycle and the meaning of compression ratio. Know how to calculate stress = force/area and strain = extension/original length, and understand the difference between tensile and compressive stress. Practise unit conversions between bar, kPa, and MPa, and between kW and hp.