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. The temperature (approximately) of the part of the flame in conta

Question

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. The temperature (approximately) of the part of the flame in contact with the boiler is (Thermal conductivity of brass = 107.4 J s − 1 m − 1 K − 1 . Heat of vaporization of water = 2256 × 1 0 3 J-kg − 1 )

TestHub · Accepted Answer

Rate of heat supplied = rate at which heat is conducted through the boiler base:
$L \frac{d m}{d t} = \frac{d Q}{d t} = \frac{K A ( θ - 100 )}{t}$
$\frac{6 \times 2256 \times 1 0 ^{3}}{60} = \frac{107.4 \times 0.15 \times ( θ - 100 )}{1 0 ^{- 2}}$
$2.256 \times 1 0^{5} = 1611 (θ - 100)$
$θ - 100 = 140$
$θ = 24 0^{\circ} C$

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