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  • A brass boiler has a base area of 0.15 m^ 2 and thickness 1.0 cm. It boils water at the rate of 6.0 kg /min when placed on a gas stove.

Q. 11.18 A brass boiler has a base area of  0.15\; m^{2} 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\times 103\; j\; kg^{-1}.

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The rate at which water boils, R = 6.0 kg min-1

The heat of vaporisation of water, L=2256\times 10^{3}\ J\ kg^{-1}

The rate at which heat enters the boiler 

\\\frac{dQ}{dT}=RL\\ \frac{dQ}{dT}=\frac{6\times 2256\times 10^{3}}{60}\\ \frac{dQ}{dT}=2.256\times 10^{5}Js^{-1}

The base area of the boiler, A = 0.15 m2

Thickness, l = 1.0 cm

Thermal conductivity of brass=109\; j\; s^{-1}m^{-1}K^{-1};

The temperature inside the boiler = Boiling point of water = 100 oC

Let the temperature of the flame in contact with the boiler be T

Amount of heat flowing into the boiler is

\\\frac{dQ}{dt}=\frac{KA\Delta T}{l}\\ 2.256\times 10^{5}=\frac{109\times 0.15\times (T-100)}{1\times 10^{-2}}\\ T-100=137.98\\ T=237.98\ ^{o}C

The temperature of the flame in contact with the boiler is 237.98 oC

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