What is the temperature around an aeroplane flying at an altitude of 4000 metres if the temperature on the earth surface is 40 ºC?

Answer Details

This question tests the concept of the environmental lapse rate, which states that temperature decreases by approximately 6.5 \(^\circ\)C for every 1000 metres of altitude gained in the troposphere.

Given information:

• Surface temperature = 40 \(^\circ\)C
• Altitude of the aeroplane = 4000 m
• Lapse rate = 6.5 \(^\circ\)C per 1000 m

Calculation:

Temperature drop = lapse rate \(\times\) altitude (in thousands of metres)

\[\text{Temperature drop} = 6.5 \times \frac{4000}{1000} = 6.5 \times 4 = 26\,^\circ\text{C}\]

Temperature at 4000 m:

\[T = 40 - 26 = 14\,^\circ\text{C}\]

The temperature around the aeroplane at 4000 metres altitude is 14 \(^\circ\)C.

Exam tip: Always use the standard environmental lapse rate of 6.5 \(^\circ\)C per 1000 m unless a different rate is specified in the question. Convert altitude to kilometres before multiplying.