Transmission Of Heat Question 50
Question: Wires A and B have identical lengths and have circular cross-sections. The radius of A is twice the radius of B $ i.e. $ $ r _{A}=2r _{B} $ . For a given temperature difference between the two ends, both wires conduct heat at the same rate. The relation between the thermal conductivities is given by
Options:
A) $ K _{A}=4K _{B} $
B) $ K _{A}=2K _{B} $
C) $ K _{A}=K _{B}/2 $
D) $ K _{A}=K _{B}/4 $
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Answer:
Correct Answer: D
Solution:
$ \frac{Q}{t}=\frac{KA\Delta \theta }{l}\Rightarrow \frac{K _{A}}{K _{B}}=\frac{A _{B}}{A _{A}}={{( \frac{r _{B}}{r _{B}} )}^{2}}=\frac{1}{4}\Rightarrow K _{A}=\frac{K _{B}}{4} $
BETA
