JEE Advanced 2023 Paper 2 Solutions

Paragraph for next two questions
A cylindrical furnace has height (H) and diameter (D) both 1m. It is maintained at temperature 360K. The air gets heated inside the furnace at constant pressure Pa and its temperature becomes T=360K. The hot air with density ρ rises up a vertical chimney of diameter d=0.1m and height h=9m above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density ρa=1.2‌kg‌m−3, pressure Pa and temperature Ta=300K enters the furnace. Assume air as an ideal gas, neglect the variations in ρ and T inside the chimney and the furnace. Also ignore the viscous effects.
[Given: The acceleration due to gravity g=10m s−2 and π=3.14 ]