Thermal Properties of Matter

Question : 20

Total: 22

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–1 when placed on a gas stove. Estimate the temperature of the part of the flame in contact with the boiler. Thermal conductivity of brass =109Js–1m–1K–1; Heat of vaporisation of water =2256×103Jkg–1.

Solution:

Here, K=109 J s−1 m−1 K−1;
A=0.15 m2;d=1.0 cm=10−2 m;
T2=100°C
t=1‌min=60s
Let T1 be the temperature of the part of boiler in contact with the stove.
Therefore, amount of heat flowing per minute through the base of the boiler,
Q=

KA (T1−T2 )

109×0.15×(T1−100)×60

10−2

Also, heat of vaporisation of water, L=2256×103 J kg−1
Rate of boiling of water in the boiler per minute
M=6.0kg=6000g
Therefore, heat received by water per minute,
Q=ML=6000×2256J

109×0.15×(T1−100)×60

0.01

=6000×2256
T1−100=

6000×2256×0.01

109×0.15×60

=138°C
or T1=138+100=238°C

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