Atmospheric lapse rate in the troposphere: If the sea-level air temperature is 15 °C, the temperature t (in °C) at height h (in metres) within the troposphere follows which standard relation?

Introduction / Context:
The International Standard Atmosphere (ISA) adopts a constant temperature lapse rate in the troposphere, the weather-bearing layer of Earth's atmosphere. This linear relation provides a handy approximation for many engineering calculations, aviation, and environmental assessments.

Given Data / Assumptions:

• Sea-level temperature taken as 15 °C.
• Standard tropospheric lapse rate: 6.5 °C per 1000 m.
• Valid only within the troposphere (up to the tropopause).

Concept / Approach:
A lapse rate of 6.5 °C per 1000 m means temperature decreases with altitude. Converting to per metre gives 0.0065 °C/m. Thus, at height h metres, subtract 0.0065 h from 15 °C to obtain the approximate air temperature.

Step-by-Step Solution:
Standard lapse: 6.5 °C per 1000 m → 0.0065 °C per m.Form relation: t(h) = 15 − 0.0065 h.Check units and sign: negative slope because temperature falls with height.Select the option matching this equation.

Verification / Alternative check:
At h = 2000 m, t = 15 − 13 = 2 °C, a realistic tropospheric estimate under standard conditions.

Why Other Options Are Wrong:
Positive slope implies warming with height, which is non-standard in the troposphere.

Alternate slopes (0.0035) do not match ISA values.

Common Pitfalls:

• Applying the relation above the tropopause where the lapse rate changes.
• Ignoring local weather inversions that deviate from the standard.

Final Answer:
t = 15 − 0.0065 h