Question

A brass boiler has a base area of 0.15 m² and a thickness of 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 vaporization of water = 2256 × 10³ J kg^–1.

Answer 1

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:
θ = \(\frac{KA(T_1-T_2)t}{I}\) .........(i)
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:
∴ mL = \(\frac{KA(T_1-T_2)t}{I}\)
T₁-T₂ = \(\frac{mLl}{KAt}\)
= \(\frac{6 \times 2256 \times 10^3 \times 0.01}{10^9 \times 0.15 \times 60}\)
= 137.98°C
Therefore, the temperature of the part of the flame in contact with the boiler is 237.98°C.