### Q.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}.

**Answer:-**

**
**Base area of the boiler,

*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 × 2256 × 10^{3} × 0.01 / (109 × 0.15 × 60)

= 137.98 ^{o} C

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