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An iron boiler is 10 mm thick and has a ...

An iron boiler is 10 mm thick and has a heating area `2m^(2)`. The two surfaces of the boiler are at `240^(@)C` and `100^(@)C` respectively. Find the mass of the water evaporated into steam per minute. Given that latest heat of steam is `536 kcal kg^(-1)` and thermal conductivity of iron is `1.6 xx 10^(-2) kcal s^(-1) m^(-1) .^(@)C^(-1)`.

Text Solution

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Here, ` x=10 mm = 10 xx 10^(-3) m , A = 2m^(2)` ,
`T_(1)=T_(2) = 240 - 100 = 140^(@)C, K = 1.6 xx 10^(-2) kcal s^(-1)m^(-1) .^(@)C^(-1)`
`L= 536 kcal kg^(-1), t = 1 mi n = 60 s`
Let m be the mass of water evaporated in steam in one minute. then `Q = mL =(KA(T_(1)-T_(2))t)/(x)`
or `m = (KA(T_(1)-T_(2))t)/(xL) = ((1.6 xx 10^(-2))xx2 xx 140 xx 60)/((10xx 10^(3))xx 536)`
`= 50.1 kg`.
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