Transmission Of Heat Question 79
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 100oC and free end of the second rod is 20oC. Then temperature of the junction is
[CPMT 1996; DPMT 1997, 03; BVP 2004]
Options:
A) 70 o C
B) 50 o C
C) 50 o C
D) 90 o 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} $
Therefore $ K _{1}=5K $ and $ K _{2}=3K $
$ \theta =\frac{5K\times 100+3K\times 20}{5K+3K} $
$ =\frac{560K}{8K} $ =70°C
BETA
