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.