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.

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.

Philoid · Accepted Answer

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 ....(1)

where, T₁ is the temperature of the flame in contact with the boiler

T₂ is the boiling point of water (= 100°C)

Heat required for boiling the water is given by

θ = mL … (2)

Equating equations (1) and (2), we get

mL = KA(T₁ - T₂)t/l

⇒ T₁ - T₂ = mLl/KAt

⇒ T₁ - T₂ = (6 kg × 2256 × 10³ J kg^-1× 0.01 m)/(109 J s^–1 m^–1 K^–1× 0.15 m²× 60 s)

⇒ T₁ - T₂ = 137.98°C

⇒ T₁ = 137.98°C + 100°C

⇒ T₁ = 237.98°C

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

NOTE: Heat of vaporisation is the amount of heat supplied to a specific quantity of the substance to change its state from a liquid to a gas at constant pressure.