Two rods of same length and cross section are joined along the length. Thermal conductivities of first and second rod are $${{K}_{1}}\,\,\text{and}\,\,{{K}_{2}}$$. The temperature of the free ends of the first and second rods are maintained at $${{\theta }_{1}}\,\,\text{and }{{\theta }_{2}}$$ respectively. The temperature of the common junction is [MP PET 2003]

Question

Two rods of same length and cross section are joined along the length. Thermal conductivities of first and second rod are $${{K}_{1}}\,\,\text{and}\,\,{{K}_{2}}$$. The temperature of the free ends of the first and second rods are maintained at $${{\theta }_{1}}\,\,\text{and }{{\theta }_{2}}$$ respectively. The temperature of the common junction is   [MP PET 2003]

TuteeHUB · Accepted Answer

$$\frac{{{K}_{2}}{{\theta }_{1}}+{{K}_{1}}{{\theta }_{2}}}{{{K}_{1}}+{{K}_{2}}}$$

TuteeHUB · Answer

$$\frac{{{\theta }_{1}}+{{\theta }_{2}}}{2}$$

TuteeHUB · Answer

$$\frac{{{K}_{2}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}({{\theta }_{1}}+{{\theta }_{2}})$$

TuteeHUB · Answer

$$\frac{{{K}_{1}}{{\theta }_{1}}+{{K}_{2}}{{\theta }_{2}}}{{{K}_{1}}+{{K}_{2}}}$$

1.	Two rods of same length and cross section are joined along the length. Thermal conductivities of first and second rod are \[{{K}_{1}}\,\,\text{and}\,\,{{K}_{2}}\]. The temperature of the free ends of the first and second rods are maintained at \[{{\theta }_{1}}\,\,\text{and }{{\theta }_{2}}\] respectively. The temperature of the common junction is [MP PET 2003]
A.	\[\frac{{{\theta }_{1}}+{{\theta }_{2}}}{2}\]
B.	\[\frac{{{K}_{2}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}({{\theta }_{1}}+{{\theta }_{2}})\]
C.	\[\frac{{{K}_{1}}{{\theta }_{1}}+{{K}_{2}}{{\theta }_{2}}}{{{K}_{1}}+{{K}_{2}}}\]
D.	\[\frac{{{K}_{2}}{{\theta }_{1}}+{{K}_{1}}{{\theta }_{2}}}{{{K}_{1}}+{{K}_{2}}}\]
Answer» D. \[\frac{{{K}_{2}}{{\theta }_{1}}+{{K}_{1}}{{\theta }_{2}}}{{{K}_{1}}+{{K}_{2}}}\]

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