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GATE 2023 AE – Question 45

Flight Mechanics & Space Dynamics · Atmosphere: Properties of the standard atmosphere · 2 marks · Multiple select

With geopotential altitude h in km and gradient dT/dh in K/m, which pairs agree with ISA?

  1. $(7,-6.5\times10^{-3})$
  2. $(9,4\times10^{-3})$
  3. $(15,0)$
  4. $(35,3\times10^{-3})$

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Correct answer: (A) $(7,-6.5\times10^{-3})$; (C) $(15,0)$; (D) $(35,3\times10^{-3})$

Explanation

The **International Standard Atmosphere (ISA)** has these layers (geopotential altitude $h$):

LayerAltitudeTemperature gradient
Troposphere0 to 11 km−6.5 K/km
Tropopause (isothermal)11 to 20 km0
Stratosphere 120 to 32 km+1.0 K/km
Stratosphere 232 to 47 km+2.8 K/km

Check the pairs (altitude in km, gradient in K/m):
- **(7, −6.5×10⁻³):** in the troposphere, −6.5 K/km. ✓
- **(9, +4×10⁻³):** at 9 km the gradient is −6.5 K/km, not +4. ✗
- **(15, 0):** in the isothermal layer. ✓
- **(35, +3×10⁻³):** in the layer where the gradient is positive (about 2.8 K/km, rounded to 3 K/km in the option). ✓

Answer **A, C and D**.