Transmission Of Heat Question 285
Question: Two rods having thermal conductivity in the ratio of 5 : 3 having equal lengths and equal cross-sectional area are joined by face to face. If the temperature of the free end of the first rod is $ 100{}^\circ C $ and free end of the second rod is $ 20^{o}C $ . Then temperature of the junction is
Options:
A) $ 70{}^\circ C $
B) $ 50{}^\circ C $
C) $ 50{}^\circ C $
D) $ 90{}^\circ C $
Show Answer
Answer:
Correct Answer: A
Solution:
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} $
$ \Rightarrow $ $ K _{1}=5K $ and $ K _{2}=3K $ $ \theta =\frac{5K\times 100+3K\times 20}{5K+3K} $
$ =\frac{560K}{8K} $
$ =70{}^\circ C $
BETA
