Question

A brass boiler has a base area of 0.15 m2 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 = 2256 × 103 J kg–1.

Answer 1

Here,
Base area of boiler ( A) = 0.15 m²
Thickness (d) = 1 cm = 10^-2 m
Rate of boiling of water (r) = 6/60 kg/s
= 0.1 kg/s
Thermal conductivity of brass ( K) = 109 J /s.m.K

Let 'T1' is the temperature of the part of the flame in contact with the boiler .

we Know,
Rate of Heat supplied = rate of heat absorbed ( utilized in vaporisation )
KA.∆T/d = mLv
KA ( T1 - 100)/d = mLv
109 × 0.15 × ( T1 - 100)/10^-2 = 0.1 × 2256 × 10³ [ Lv = 2256 × 10³ J/kg ]
1635( T1 - 100) = 225600
T1 = 225600/1635 + 100
= 137.98 + 100
= 237.98°C

Answer 2

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