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 $$P_a$$ 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 $$h = 9$$ m above the furnace and exits the chimney. As a result, atmospheric air of density $$\rho_a = 1.2$$ kg m$$^{-3}$$, pressure $$P_a$$ and temperature $$T_a = 300$$ 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 $$g = 10$$ ms$$^{-2}$$ and $$\pi = 3.14$$]