A cylindrical furnace has height (H) and diameter (D) both 1 m. It is maintained at temperature 360 K. The air gets heated inside the furnace at constant pressure Pa and its temperature becomes T = 360 K. The hot air with density  $\rho$  rises up a vertical chimney of diameter d = 0.1 m and height h = 8 m above the furnace and exits the chimney (see the figure). As a result, atmospheric air of density  ${\rho }_a=1.2kg{m}^{-3}$ , pressure  $P_a$  and temperature  $T_a=300k$  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. Assume atmospheric pressure  $P_a$  at base of furnace outside the structure. [Given : The acceleration due to gravity  $g=10m{s}^{-2}\text{\hspace{0.33em}and\hspace{0.17em}\hspace{0.17em}}\pi =3.14$]