In a high ceiling hall, a fire occurs with a heat release rate of $1500$ kW on a floor area of $2$ m$2.$ The mechanical smoke ventilation at the ceiling starts by means of a heat detector located at the ceiling exactly above the centre of the fire. The heat detector is activated and consequently start the mechanical smoke ventilation if the smoke temperature rise is greater than $$T $=40$C$.$ Assuming that ambient temperature is $22$C$,$ propose the height of the hall ceiling which at the proposed height, the smoke ventilator will be activated.