Transmission Of Heat Question 322
Question: Water is being boiled in a flat bottom kettle placed on a stove. The area of the bottom is $ 3000cm^{2} $ and the thickness is 2 mm. If the amount of steam produced is 1 g/min. Calculate the difference of temperature between the inner and outer surface of the bottom. Thermal conductivity for the material of kettle is $ 0.5,cal/{{,}^{o}}C/s/cm $ and the latent heat of steam is 540 cal/gm.
Options:
A) $ 1.2\times {{10}^{-3}}{{,}^{o}}C $
B) $ 2.4\times {{10}^{-3}}{{,}^{o}}C $
C) $ 3.6\times {{10}^{-3}}{{,}^{o}}C $
D) $ 4.8\times {{10}^{-3}}{{,}^{o}}C $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Mass of steam produced, $ \frac{dm}{dt}=\frac{1}{60}g/s $ . Hence heat transferred per sec to water $ \frac{\Delta Q}{\Delta t}=L _{v}\frac{dm}{dt}=\frac{KA\theta }{d} $ where $ \theta $ is the required temperature difference
$ \Rightarrow $ $ \theta =\frac{540\times \frac{1}{60}\times 0.2\times {{10}^{-3}}}{0.5\times 3000}=1.2\times {{10}^{-3}}{{,}^{0}}C $
BETA
