A brass boiler has a base 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 `=109" Js"^(-1)m^(-1)K^(-1),` Heat of vaporization of water `=2256xx10^(3)" Jkg"^(-1)`.

Explanation

Heat entered from bottom of boiler in one second,
`(Q)/(t)=KA(dT)/(dx)`
`=109xx0.15xx(T_(1)T_(2))/(dx)`
`=109xx0.15xx(T_(1)-100)/(1xx10^(-2))" "[becauset=1s]`
`Q=1635(T_(1)-100)J` . . . (1)
Rate of heating water in boiler,
`(M)/(t)=6.0(kg)/("min")=(6.0)/(60)=0.1" kgs"^(-1)`
Rate of heat obtained by water,
`(Q.)/(t)=(M)/(t)L.`
`:.Q.="ML".`
`=0.1xx2256xx10^(3)`
`=2256xx10^(2)J` . . . (2)
From equation (1) and (2), `Q=Q.`
`:.1635(T_(1)=100)=225600`
`:.T_(1)-100=(225600)/(1635)`
`:.T_(1)=138+100`
`:.T_(1)=238^(@)C`