Abrass boiler has a base area of 0.15 m²and thickness 1.0 cm. It boils waterat the rate of 6.0 kg/min when placed on a gas stove. Estimate thetemperature of the part of the flame in contact with the boiler.Thermal conductivity of brass = 109 J s ^–1m^–1K^–1;Heat of vaporisation of water = 2256 × 10³J kg^–1.

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Solution

Basearea of the boiler, A =0.15 m²
Thicknessof the boiler, l =1.0 cm = 0.01 m
Boilingrate of water, R= 6.0 kg/min
Mass,m = 6 kg
Time,t = 1 min= 60 s
Thermalconductivity of brass, K= 109 J s ^–1m^–1K^–1
Heatof vaporisation, L= 2256 × 10³J kg^–1
Theamount of heat flowing into water through the brass base of theboiler is given by:
Where,
T₁= Temperature of the flame in contact with the boiler
T₂= Boiling point of water = 100°C
Heatrequired for boiling the water:
θ =mL … (ii)
Equatingequations (i)and (ii),we get:
Therefore,the temperature of the part of the flame in contact with the boileris 237.98°C.

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