__Question 11.20__:
A
brass boiler has a base area of 0.15 m

^{2}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 × 10^{3}J kg^{–1}.

__Solution__:*A*= 0.15 m

^{2}

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 × 10

^{3}J kg

^{–1}

The amount of heat flowing into water through the brass base of the boiler is given by:

θ = KA(T

_{1}- T

_{2}) t / l ....(i)

Where,

*T*

_{1}= Temperature of the flame in contact with the boiler

*T*

_{2}= Boiling point of water = 100°C

Heat required for boiling the water:

θ =

*mL*… (

*ii*)

Equating equations (

*i*) and (

*ii*), we get:

∴ mL = KA(T

_{1}- T

_{2}) t / l

T

_{1}- T

_{2}= mLl / KAt

= 6 X 2256 X 10

^{3}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.

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