Thermal Properties of Matter NCERT Solutions Class 11 Physics - Solved Exercise Question 11.20

Question 11.20:

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:

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:
θ = mL … (ii)
Equating equations (i) and (ii), we get:
∴ mL = KA(T₁ - T₂) t / l
T₁ - T₂ = mLl / KAt
= 6 X 2256 X 10³ X 0.01 / (109 X 0.15 X 60)
= 137.98 ^o C
Therefore, the temperature of the part of the flame in contact with the boiler is 237.98°C.