Transmission Of Heat Question 113
Question: Three rods of same dimensions are arranged as shown in figure they have thermal conductivities $ K _{1},K _{2} $ and$ K _{3} $ The points P and Q are maintained at different temperatures for the heat to flow at the same rate along PRQ and PQ then which of the following option is correct
[KCET 2001]
Options:
A) $ K _{3}=\frac{1}{2}(K _{1}+K _{2}) $
B) $ K _{3}=K _{1}+K _{2} $
C) $ K _{3}=\frac{K _{1}K _{2}}{K _{1}+K _{2}} $
D) $ K _{3}=2(K _{1}+K _{2}) $
Show Answer
Answer:
Correct Answer: C
Solution:
The given arrangement of rods can be redrawn as follows It is given that H1 = H2
Therefore $ \frac{KA({\theta _{1}}-{\theta _{2}})}{2l}=\frac{K _{3}A({\theta _{1}}-{\theta _{2}})}{l} $
Therefore $ K _{3}=\frac{K}{2}=\frac{K _{1}K _{2}}{K _{1}+K _{2}} $
BETA
