Temperature, Pressure, Density and the Gas Laws
Temperature is a measure of mean molecular kinetic energy. Candidates should be fluent in Celsius, Kelvin and Fahrenheit conversion (K = °C + 273.15) and in the meaning of dry adiabatic lapse rate (DALR ≈ 3 °C/1000 ft), saturated adiabatic lapse rate (SALR, variable, roughly 1.5–2 °C/1000 ft in warm moist air) and environmental lapse rate (ELR).
Gas laws and density
Boyle's law: pV = constant at constant temperature. Charles's law: V/T = constant at constant pressure. The combined gas law and the equation of state p = ρRT tie pressure, density and temperature together. Density therefore falls with increasing altitude, increasing temperature and increasing humidity (moist air is less dense than dry air because water vapour is lighter than the average molecular mass of air - a classic trap).
Aviation consequences
High temperature, high altitude and high humidity all reduce density and thus reduce lift, thrust and propeller efficiency while increasing true airspeed for a given IAS and lengthening take-off and landing runs. Pressure altitude and density altitude are the operational quantities: density altitude is pressure altitude corrected for temperature.
Worked example: an airfield at 2000 ft pressure altitude on a day 15 °C warmer than ISA has density altitude of roughly 2000 + (15 × 120) = 3800 ft, i.e. the aircraft behaves as if at 3800 ft.
Trap: the rule-of-thumb factor is 120 ft per °C of ISA deviation, not 100 or 150.