Question

A brass boiler has a base area of $0.15m^2$ 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 $=109J{s}^{-1}{m}^{-1}{K}^{-1}$; Heat of vaporisation of water $=2256\times {10}^{3}Jk{g}^{-1}$.

Answer 1

Base area of the boiler, $A=0.15m^2$

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, $K=109J{s}^{-1}{m}^{-1}{k}^{-1}$

Heat of vaporisation, $L=2256\times {10}^{3}Jk{g}^{-1}$
The amount of heat flowing into water through the brass base of the boiler is given by:

$\theta =KA(T_1-T_2)t/l$ .... (i)

where,
$T_1=$ Temperature of the flame in contact with the boiler
$T_2=$ Boiling point of water $={100}^{o}C$
Heat required for boiling the water:

$\theta =mL$ .... (ii)
Equating equations (i) and (ii), we get:

$\therefore mL=KA(T_1-T_2)t/l$
$T_1-T_2=mLl/KAt$
$=6\times 2256\times {10}^3\times 0.01/(109\times 0.15\times 60)$
$={137.98}^{o}C$
Therefore, the temperature of the part of the flame in contact with the boiler is ${237.98}^{o}C$.