Expert-level engineering thermodynamics covering laws of thermodynamics, thermodynamic cycles, steam power plants, refrigeration, gas dynamics, and combustion.
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First law: energy is conserved, delta U = Q minus W for closed system. Second law: entropy of universe increases for irreversible processes. Entropy: ds = dQ_rev over T, measure of irreversibility. Exergy: maximum useful work from system brought to equilibrium with environment.
Rankine cycle: steam power plant, boiler, turbine, condenser, pump. Rankine efficiency: improved by superheat, reheat, and regeneration. Brayton cycle: gas turbine, compressor, combustor, turbine. Brayton efficiency: eta = 1 minus 1 over r_p to the power k-1 over k. Combined cycle: gas turbine exhaust heats steam Rankine, 60% efficiency possible.
Vapor compression: compressor, condenser, expansion valve, evaporator. COP: coefficient of performance, QL over W_net for refrigerator. Heat pump COP: QH over W_net, always greater than refrigerator COP by one. Carnot COP: maximum possible COP for given temperature limits.
Mach number: M = V over speed of sound, speed of sound = sqrt of gamma R T. Isentropic relations: T2 over T1 = P2 over P1 to the k-1 over k power. Normal shock: supersonic to subsonic, sudden pressure rise, entropy increase. Nozzle flow: converging accelerates to M=1 at throat, diverging to supersonic.
| Pitfall | Fix |
|---|---|
| Sign convention errors | Define positive Q in and positive W out at start |
| Using ideal gas for steam | Use steam tables for accurate properties |
| Ignoring pump work in Rankine | Include pump work even though small compared to turbine |
| Adiabatic assumption for non-insulated system | Only apply adiabatic if process is fast or well-insulated |
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Expert-level abstract algebra knowledge. Use when working with groups, rings, fields, modules, Galois theory, representation theory, or algebraic structures. Also use when the user mentions 'group', 'ring', 'field', 'homomorphism', 'isomorphism', 'normal subgroup', 'quotient group', 'Sylow theorem', 'Galois theory', 'polynomial ring', 'ideal', 'module', 'vector space', or 'representation theory'.
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Expert-level acoustics knowledge. Use when working with sound waves, acoustic propagation, resonance, standing waves, Doppler effect, room acoustics, ultrasound, noise control, musical acoustics, or architectural acoustics. Also use when the user mentions 'sound wave', 'decibel', 'frequency', 'resonance', 'standing wave', 'Doppler effect', 'acoustic impedance', 'reverberation', 'ultrasound', 'noise control', 'harmonics', or 'sound intensity'.
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Expert-level aerodynamics covering subsonic and supersonic flow, lift and drag, airfoil theory, boundary layers, compressible flow, and CFD methods.
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Expert-level air quality engineering covering pollutant sources, atmospheric dispersion, air quality standards, emission controls, and air quality modeling.
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Expert-level aircraft structures covering structural design philosophy, wing and fuselage analysis, fatigue and damage tolerance, composite structures, and certification.
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Expert-level algorithms and complexity theory covering sorting, searching, graph algorithms, dynamic programming, greedy algorithms, NP-completeness, and algorithm design paradigms.
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