Transmission Of Heat Question 286
Question: A wall has two layers A and B made of different materials. The thickness of both the layers is the same. The thermal conductivity of A and B are $ K _{A} $ and $ K _{B} $ such that $ K _{A}=3K _{B} $ . The temperature across the wall is $ 20{}^\circ C $ . In thermal equilibrium
Options:
A) The temperature difference across $ A=15{}^\circ C $
B) The temperature difference across $ A=5{}^\circ C $
C) The temperature difference across A is $ 10{}^\circ C $
D) The rate of transfer of heat through A is more than that through B.
Show Answer
Answer:
Correct Answer: B
Solution:
In series rate of flow of heat is same
$ \Rightarrow $ $ \frac{K _{A}A({\theta _{1}}-\theta )}{l}=\frac{K _{B}A(\theta -{\theta _{2}})}{l} $
$ \Rightarrow $ $ 3K _{B}({\theta _{1}}-\theta )=K _{B}(\theta -{\theta _{2}}) $
$ \Rightarrow $ $ 3({\theta _{1}}-\theta )=(\theta -{\theta _{2}}) $
$ \Rightarrow $ $ 3{\theta _{1}}-3\theta =\theta -{\theta _{2}} $
$ \Rightarrow $ $ 4{\theta _{1}}-4\theta ={\theta _{1}}-{\theta _{2}} $
$ \Rightarrow $ $ 4({\theta _{1}}-\theta )=({\theta _{1}}-{\theta _{2}}) $
$ \Rightarrow $ $ 4({\theta _{1}}-\theta )=20 $
$ \Rightarrow $ $ ({\theta _{1}}-\theta )=5{}^\circ C $
BETA
