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A brass boiler has a base area of 0.15 m...

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` = 2256xx 10^(3) J kg^(–1)`.

Text Solution

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Let `T_(1)` be the temperature of the part of the flame in contact with boiler. The amount of heat flown into water in 1 minute
`Q=(KA(theta_(1)-theta_(2))t)/l=(109xx0.15xx(T_(1)-100)xx60)/0.01`
Mass of water boiled in 1 minute = 6kg = 6000g.
Heat required to boil the water, Q = mL = `6000xx2256`
`therefore(109xx0.15xx(T_(1)-100)xx60)/0.01=6000xx2256`
(or) `T_(1)-100=138" "thereforeT_(1)=238^(@)C`
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