A boiler with $65\%$ efficiency absorbs $10000k\frac{J}{s}$ of heat when fed with coal of $HHV30,000K\frac{J}{k}g.$ Ambient air at

atmospheric pressure and temperature of $24C.$ The flue gas pressure is $125$kPa, average temperature of $150C,$

velocity of $4\frac{m}{s}$ and a molecular weight of $30.$ The fuel is burned with $100\%$ excess air and ash produced is $0\mathrm{.}50\%$

of the flue gas. Determine:

a$)$ Diameter of chimney $(m)$

b$)$ Height of chimney $($m$)$