Ncert Exercises & Solutions

11.20:
A brass boiler has a base area of 0.15 $m^{2}$ and thickness 1.0 cm. It boils water at a 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 × $10^{3}$ J/kg.

It is given in the question that:

Thermal conductivity of brass, K = 109 J s $^{- 1}$ m–1 K $^{- 1}$

Heat of vaporisation, L = 2256 × 103 J kg $^{- 1}$

The amount of heat flowing into the water through the brass base of the boiler:

$Q_{1} = \frac{KA (T_{1} - T_{2}) t}{l}$

Where,

$T_{1}$ = Temperature of the flame in contact with the boiler

T $_{2}$ = Boiling point of water = 100°C

The heat required for boiling the water:

$Q_{2} = mL$

Amount of heat flowing into the water = Amount of heat required to boil the water

$\Rightarrow mL = \frac{LA (T_{1} - T_{2}) t}{l}$
$\Rightarrow T_{1} - T_{2} = \frac{mLl}{KAt}$
$= \frac{6 \times 2256 \times 10^{3} \times 0.01}{109 \times 0.15 \times 60}$
$= 137.98 ° c$

Therefore, the temperature of the part of the flame in contact with the boiler is 237.98 °C.

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