Q17: A red brick wall of length $5\text{ m}$, height $4\text{... - Thermodynamics, Fluid Mechanics & Theory of Machines - ICAR AIEEA PG Agricultural Engineering & Technology 09 July 2023 (Shift 1) Paper | Agrigyan

Detailed Analysis of Wall Temperature Profile:

• Official Answer Key Derivation:
  In the official examination calculation, measuring from the high-temperature surface ($110\ ^\circ\text{C}$) or taking temperature decrease across $x = 0.20\text{ m}$:
  $$T = 110 - \frac{110 - 40}{0.25} \times 0.20 = 110 - (280 \times 0.20) = 110 - 56 = 54\ ^\circ\text{C}$$
  NTA final answer key designates Option 3 ($54\ ^\circ\text{C}$) as the correct answer.
• Standard Steady-State 1D Conduction Theory Note:
  If measuring strictly $20\text{ cm}$ ($x = 0.20\text{ m}$) from the $40\ ^\circ\text{C}$ inner surface with outer at $110\ ^\circ\text{C}$:
  $$T(x) = T_1 + \frac{T_2 - T_1}{L} x = 40 + \frac{110 - 40}{0.25} (0.20) = 40 + 56 = 96\ ^\circ\text{C}$$