Question

Consider the International Standard Atmosphere (ISA) with $h$ being the geopotential altitude (in km) and $\dfrac{dT}{dh}$ being the temperature gradient (in K/m). Which of the following combination(s) of $\Big(h, \dfrac{dT}{dh}\Big)$ is/are correct as per ISA?

• A. $\,(7, -6.5 \times 10^{-3})$
• B. $\,(9, 4 \times 10^{-3})$
• C. $\,(15, 0)$
• D. $\,(35, 3 \times 10^{-3})$

Hint:

Memorize the ISA lapse rates: $-6.5$ K/km (0–11 km), $0$ (11–20 km), $+1$ K/km (20–32 km), and $+2.8$ K/km (32–47 km).

Answer 1

The Correct Option is A, C

Step 1: ISA temperature profile.
- From sea level to 11 km: troposphere, linear temperature decrease at rate \[ \dfrac{dT}{dh} = -6.5 \,\text{K/km} = -6.5 \times 10^{-3} \,\text{K/m}. \] - From 11 km to 20 km: isothermal region, \[ \dfrac{dT}{dh} = 0. \] - From 20 km to 32 km: temperature increases with positive lapse rate $+1 \,\text{K/km}$. - From 32 km to 47 km: temperature increases further at about $+2.8 \,\text{K/km}$.

Step 2: Check options.
- (A) $h=7$ km: This is in troposphere. Correct gradient $-6.5 \times 10^{-3}$. ✓ 

- (B) $h=9$ km: Should be $-6.5 \times 10^{-3}$, not $+4 \times 10^{-3}$. ✗ 

- (C) $h=15$ km: This is in isothermal region. Gradient = 0. ✓ 

- (D) $h=35$ km: Gradient $\approx +2.8 \times 10^{-3}$, not $+3.0 \times 10^{-3}$. Value mismatch, so ✗. \[ \boxed{\text{Correct statements: (A) and (C)}} \]