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A brass boiler has a base area of 0.15 m2and 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.

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Base area of the boiler, A = 0.15 m2 Thickness of the boiler, l = 1.0 cm = 0.01 m Boiling rate of water, R = 6.0 kg/min Mass, m = 6 kg Time, t = 1 min = 60 s 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...
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Base area of the boiler, A = 0.15 m2

Thickness of the boiler, l = 1.0 cm = 0.01 m

Boiling rate of water, R = 6.0 kg/min

Mass, m = 6 kg

Time, t = 1 min = 60 s

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 water through the brass base of the boiler is given by:

Where,

T1 = Temperature of the flame in contact with the boiler

T2 = Boiling point of water = 100°C

Heat required for boiling the water:

θ = mL … (ii)

Equating equations (i) and (ii), we get:

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

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