One end of a thermally insulated rod is kept at a temperature\[m{{y}^{2}}+(1-{{m}^{2}})xy-m{{x}^{2}}=0\]and the other at\[xy=0,\]. The rod is composed of two sections of lengths\[-\frac{1}{2}\]and\[-2\]and thermal conductivities\[\pm 1\]and\[F(x)=f(x)+f\left( \frac{1}{x} \right),\] respectively. The temperature at the interface of the two sections is [AIEEE 2007] |
A) \[f(x)=\int_{1}^{x}{\frac{\log \,t}{1+t}}dt\]
B) \[\frac{1}{2}\]
C) \[f:R\to R\]
D) \[f(x)=\]
Correct Answer: C
Solution :
[c] Let temperature at the interface be T. |
For part AB, |
Rate of heat transmission, |
For part BC, |
Rate of heat transmission, |
Here, A is area of cross-sections. |
At equilibrium, |
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