Transmission Of Heat Question 328
Question: Two rods having thermal conductivities in the ratio of 5 : 3 having equal lengths and equal cross-sectional area are joined in series. If the temperature of the free end of the first rod is $ 100^{o}C $ and free end of the second rod is $ 20^{o}C $ . Then temperature of the junction is
Options:
A) $ ~70^{o}C $
B) $ ~60^{o}C $
C) $ 50^{o}C $
D) $ 90^{o}C $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Temperature of interface $ \theta =\frac{k _{1}{\theta _{1}}+k _{2}{\theta _{2}}}{k _{1}+k _{2}} $ It is given that $ \frac{K _{1}}{K _{2}}=\frac{5}{3} $ Let $ K _{1}=5K $ and $ K _{2}=3K $
$ \Rightarrow $ $ \theta =\frac{5K\times 100+3K\times 20}{5K+3K} $
$ \Rightarrow $ $ \theta =\frac{560K}{8K}=70{{,}^{o}}C $
$ \
Therefore $ $ \theta =70{{,}^{o}}C $
BETA
