For International Standard Atmosphere (ISA) up to $11\text{ km}$, which of the following statement(s) is/are true?
Scientific schematic diagram reproduced from official IIT paper
Options:
(A) The hydrostatic / aerostatic equation is used
(B) The temperature lapse rate is taken as $-10^{-2}\text{ K/m}$
(C) The sea level conditions are taken as: pressure, $p_0 = 1.01325 \times 10^5\text{ Pa}$; temperature, $T_0 = 300\text{ K}$; density, $\rho_0 = 1.225\text{ kg/m}^3$
(D) Air is treated as a perfect gas
Official Answer Key:
A, D
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2022 Q.27)**
**1. Standard Atmosphere Hypotheses**:
- Hydrostatic equation $dp = -\rho g \, dh$ is fundamental (Option A is TRUE).
- Ideal gas equation of state $p = \rho R T$ is applied (Option D is TRUE).
- Standard lapse rate in troposphere is $-6.5 \times 10^{-3}\text{ K/m}$ (not $-10^{-2}$).
- Sea level standard temperature is $288.15\text{ K}$ (not $300\text{ K}$).
- **Official Answer Key**: **A, D**
