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A brass boiler has a base area of $0.15 \mathrm{~m}^2$ and thickness $1.0 \mathrm{~cm}$. It boils water at the rate of $6.0 \mathrm{~kg} / \mathrm{min}$, when placed on a gas stove. Estimate the temperature of the part of the flame in contact with the boiler. Thermal conductivity of brass $=109 \mathrm{~J} \mathrm{~s}^{-1} \mathrm{~m}^{-1} \mathrm{k}^{-1}$. Heat of vaporisation of water $=2256 \times 10^3 \mathrm{~J} \mathrm{k}^{-1} \mathrm{~g}^{-1}$
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Verified Answer
$A=0.15 \mathrm{~m}^2, \Delta x=1 \mathrm{~cm}=0.01 \mathrm{~m}$
Transfer of heat $\frac{Q}{t}=\frac{6 \mathrm{~kg}}{\min }=\frac{1}{10} \mathrm{~kg} / \mathrm{s}$
$\because \quad \frac{\Delta Q}{\Delta t}=k A\left(\frac{\Delta T}{\Delta x}\right)$
$\Rightarrow \frac{2256 \times 10^3}{10}=6.09 \times 0.15 \times \frac{t-100}{0.01}$
$\Rightarrow \quad t-100=\frac{2256}{609 \times 0.15}=24.7$
$t=124.7^{\circ} \mathrm{C}$
Transfer of heat $\frac{Q}{t}=\frac{6 \mathrm{~kg}}{\min }=\frac{1}{10} \mathrm{~kg} / \mathrm{s}$
$\because \quad \frac{\Delta Q}{\Delta t}=k A\left(\frac{\Delta T}{\Delta x}\right)$
$\Rightarrow \frac{2256 \times 10^3}{10}=6.09 \times 0.15 \times \frac{t-100}{0.01}$
$\Rightarrow \quad t-100=\frac{2256}{609 \times 0.15}=24.7$
$t=124.7^{\circ} \mathrm{C}$
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