| Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are \[{{K}_{1}}\] and \[{{K}_{2}}\]. The thermal conductivity of the composite rod will be [NEET-2017] |
 |
A) \[2({{K}_{1}}+{{K}_{2}})\]
B) \[\frac{{{K}_{1}}+{{K}_{2}}}{2}\]
C) \[\frac{3({{K}_{1}}+{{K}_{2}})}{2}\]
D) \[{{K}_{1}}+{{K}_{2}}\]
Correct Answer: B
Solution :
| [b] Thermal current |
| \[H={{H}_{1}}+{{H}_{2}}\] |
| \[=\frac{{{K}_{1}}A({{T}_{1}}-{{T}_{2}})}{d}+\frac{{{K}_{2}}A({{T}_{1}}-{{T}_{2}})}{d}\] |
| \[\frac{{{K}_{EQ}}2A({{T}_{1}}-{{T}_{2}})}{d}=\frac{A({{T}_{1}}-{{T}_{2}})}{d}[{{K}_{1}}+{{K}_{2}}]\] |
| \[{{K}_{EQ}}=\left[ \frac{{{K}_{1}}+{{K}_{2}}}{2} \right]\] |
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