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.
Solution
Given,
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 = KA(T1 - T2) t / l ...(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 is,
θ = mL … (ii)
Now, on equating equations (i) and (ii), we get
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 = KA(T1 - T2) t / l ...(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 is,
θ = mL … (ii)
Now, on equating equations (i) and (ii), we get
Therefore, temperature for the part of the flame in contact with the burner is 137.98o C
