Two walls of thicknesses d1 and d2 and thermal conductivities k1 and k2 are in contact. In the steady state, if the temperatures at the outer surfaces are $${{T}_{1}}$$ and $${{T}_{2}}$$, the temperature at the common wall is [MP PMT 1990; CBSE PMT 1999]

Question

Two walls of thicknesses d1 and d2 and thermal conductivities k1 and k­2 are in contact. In the steady state, if the temperatures at the outer surfaces are $${{T}_{1}}$$ and $${{T}_{2}}$$, the temperature at the common wall is [MP PMT 1990; CBSE PMT 1999]

TuteeHUB · Accepted Answer

$$\frac{{{k}_{1}}{{T}_{1}}+{{k}_{2}}{{d}_{2}}}{{{d}_{1}}+{{d}_{2}}}$$

TuteeHUB · Answer

$$\frac{{{k}_{1}}{{T}_{1}}{{d}_{2}}+{{k}_{2}}{{T}_{2}}{{d}_{1}}}{{{k}_{1}}{{d}_{2}}+{{k}_{2}}{{d}_{1}}}$$

TuteeHUB · Answer

$$\left( \frac{{{k}_{1}}{{d}_{1}}+{{k}_{2}}{{d}_{2}}}{{{T}_{1}}+{{T}_{2}}} \right){{T}_{1}}{{T}_{2}}$$

TuteeHUB · Answer

$$\frac{{{k}_{1}}{{d}_{1}}{{T}_{1}}+{{k}_{2}}{{d}_{2}}{{T}_{2}}}{{{k}_{1}}{{d}_{1}}+{{k}_{2}}{{d}_{2}}}$$

1.	Two walls of thicknesses d1 and d2 and thermal conductivities k1 and k2 are in contact. In the steady state, if the temperatures at the outer surfaces are \[{{T}_{1}}\] and \[{{T}_{2}}\], the temperature at the common wall is [MP PMT 1990; CBSE PMT 1999]
A.	\[\frac{{{k}_{1}}{{T}_{1}}{{d}_{2}}+{{k}_{2}}{{T}_{2}}{{d}_{1}}}{{{k}_{1}}{{d}_{2}}+{{k}_{2}}{{d}_{1}}}\]
B.	\[\frac{{{k}_{1}}{{T}_{1}}+{{k}_{2}}{{d}_{2}}}{{{d}_{1}}+{{d}_{2}}}\]
C.	\[\left( \frac{{{k}_{1}}{{d}_{1}}+{{k}_{2}}{{d}_{2}}}{{{T}_{1}}+{{T}_{2}}} \right){{T}_{1}}{{T}_{2}}\]
D.	\[\frac{{{k}_{1}}{{d}_{1}}{{T}_{1}}+{{k}_{2}}{{d}_{2}}{{T}_{2}}}{{{k}_{1}}{{d}_{1}}+{{k}_{2}}{{d}_{2}}}\]
Answer» B. \[\frac{{{k}_{1}}{{T}_{1}}+{{k}_{2}}{{d}_{2}}}{{{d}_{1}}+{{d}_{2}}}\]

Two walls of thicknesses d1 and d2 and thermal conductivities k1 and k2 are in contact. In the steady state, if the temperatures at the outer surfaces are \[{{T}_{1}}\] and \[{{T}_{2}}\], the temperature at the common wall is [MP PMT 1990; CBSE PMT 1999]

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Two walls of thicknesses d1 and d2 and thermal conductivities k1 and k­2 are in contact. In the steady state, if the temperatures at the outer surfaces are \[{{T}_{1}}\] and \[{{T}_{2}}\], the temperature at the common wall is [MP PMT 1990; CBSE PMT 1999]

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Two walls of thicknesses d1 and d2 and thermal conductivities k1 and k2 are in contact. In the steady state, if the temperatures at the outer surfaces are \[{{T}_{1}}\] and \[{{T}_{2}}\], the temperature at the common wall is [MP PMT 1990; CBSE PMT 1999]