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.

Asked by Abhisek | 1 year ago |  201

Solution :-

Base area of the brass boiler, A= 0.15 m2

Thickness of the boiler, d =1.0 cm=0.01 m
Brass boiler boils water at the rate, R=6.0 kg/min

Time, t = 60 sec

Mass = 6 kg

Thermal conductivity of brass, K =109 Js−1m−1k−1

Heat of vaporisation of water, L = 2256×103 Jkg−1

Let  T1  Temperature of the flame in contact with the boiler

Let T2 be the boiling point of water = 100°C

The Q be the amount of heat flowing into water through the base of the boiler
Q =$$\dfrac{KA(T_1 −T_2)t}{d}$$

Q = $$\dfrac{109 \times 0.15 \times (T_1 – 100) \times 60}{0.01}$$ ..........(1)

Q=mL

Q = 6 x 2256×103 ——-(2)

Equating equations (1) and (2), we get:
mL  = $$\dfrac{KA(T_1 −T_2)t}{d}$$

6 x 2256×103

$$\dfrac{ [10^9 \times 0.15 \times (T_1 – 100) \times 60]}{ 0.01}$$

​13536 ×103 x 0.01 = 981 (T1 – 100)

T1 – 100 = $$\dfrac{ 13536 ×10^3 \times 0.01}{ 981}$$

T1 = 137.9 + 100

= 237. 9°C

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

Answered by Pragya Singh | 1 year ago

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