JEE Advanced 2023 Paper 2 Solutions

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