Temperature, Pressure, Density and Their Altimetry Implications
The relationships to master
Temperature, pressure and density are linked by the gas law: at constant pressure, warmer air is less dense, and at constant temperature, higher pressure means denser air. Density altitude is the single most examined idea: it is pressure altitude corrected for temperature. High elevation, high temperature, high humidity and low pressure all raise density altitude and degrade aircraft and engine performance. Humidity is the classic trap: moist air is less dense than dry air at the same temperature and pressure, because water vapour molecules are lighter than the nitrogen and oxygen they displace.
Altimeter errors
An altimeter is a pressure instrument calibrated to the ISA. Set QNH and it reads elevation when on the ground; set QFE and it reads height above the reference; set 1013.25 hPa (standard) and it reads pressure altitude, used above the transition altitude. Learn the direction of errors. Fly from high pressure to low pressure without resetting: the aircraft is lower than the altimeter shows, a dangerous trap. Fly from warm to cold air: true altitude is lower than indicated, the "high to low, look out below" mnemonic. Cold-air correction adds height to minima in very cold conditions.
Worked example
Pressure altitude 10,000 ft, temperature 20°C. ISA temperature there is 15 - 20 = -5°C, so the air is 25°C warmer than standard. Using roughly 120 ft per degree of ISA deviation, density altitude is about 10,000 + (25 × 120) = 13,000 ft. Expect noticeably longer take-off and climb distances.