Two walls of thicknesses d_1 and d_2 and thermal conductivities k_1 and k_2 are in contact. In the steady state, if the temperatures at the

Q: Two walls of thicknesses $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$ 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

a (a) In series both walls have same rate of heat flow. Therefore $\frac{{dQ}}{{dt}} = \frac{{{K_1}A({T_1} - \theta )}}{{{d_1}}} = \frac{{{K_2}A(\theta - {T_2})}}{{{d_2}}}$ $ \Rightarrow {K_1}{d_2}({T_1} - \theta ) = {K_2}{d_1}(\theta - {T_2})$ $ \Rightarrow \theta = \frac{{{K_1}{d_2}{T_1} + {K_2}{d_1}{T_2}}}{{{K_1}{d_2} + {K_2}{d_1}}}$

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

Two walls of thicknesses $d_1$ and $d_2$ and thermal conductivities $k_1$ and $k_2$ 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

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$\frac{{{k_1}{d_1}{T_1} + {k_2}{d_2}{T_2}}}{{{k_1}{d_1} + {k_2}{d_2}}}$

Medium

STD 11 Science
NEET
STD 11 - 10.2. transmission of heat
Physics

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