.A brass boiler has a base area of 0.15 m2 and thickness 1.0 cm. It boils water at the rate of 6.0 kg/min when placed on a gas stove. Estimate the temperature of the part of the flame in contact with the boiler. Thermal conductivity of brass = 109 J s–1 m–1 K–1; Heat of vaporisation of water = 2256 × 103 J kg–1.
Base area of the boiler, A=0.15m2 Thickness of the boiler, l=1.0cm=0.01m Boiling rate of water, R=6.0kg/min Mass, m=6kg Time, t = 1 min = 60 s Thermal conductivity of brass, K=109Js−1m−1k−1 Heat of vaporisation, L=2256×103Jkg−1 The amount of heat flowing into water through the brass base of the boiler is given by: θ=KA(T1−T2)t/l .... (i) where, T1= Temperature of the flame in contact with the boiler T2= Boiling point of water =100oC Heat required for boiling the water: θ=mL .... (ii) Equating equations (i) and (ii), we get: ∴mL=KA(T1−T2)t/l T1−T2=mLl/KAt =6×2256×103×0.01/(109×0.15×60) =137.98oC Therefore, the temperature of the part of the flame in contact with the boiler is 237.98oC.
