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10-2.Transmission of Heat
normal
Two plates of same thickness of coefficients of thermal conductivities $K_1$ and $K_2$ and areas of cross section $A_1$ and $A_2$ are connected as shown. The effective coefficient of thermal conductivity $K$.
A
$K_1A_1 + K_2A_2$
B
$\frac{{{K_1}{A_1} + {K_2}{A_2}}}{{{A_1} + {A_2}}}$
C
$\frac{{{K_1}{A_2} + {K_2}{A_1}}}{{{A_1} + {A_2}}}$
D
$\frac{{{K_1}{A_1}}}{{{K_2}{A_2}}}$
Solution
$\frac{1}{\mathrm{R}_{\mathrm{ea}}}=\frac{1}{\mathrm{R}_{1}}+\frac{1}{\mathrm{R}_{2}}$
$\frac{\mathrm{K}_{\mathrm{eq}}\left(\mathrm{A}_{1}+\mathrm{A}_{2}\right)}{\ell}=\frac{\mathrm{K}_{1} \mathrm{A}_{1}}{\ell}+\frac{\mathrm{K}_{2} \mathrm{A}_{2}}{\ell}$
$\mathrm{K}_{\mathrm{eq}}=\frac{\mathrm{K}_{1} \mathrm{A}_{1}+\mathrm{K}_{2} \mathrm{A}_{2}}{\mathrm{K}_{1}+\mathrm{K}_{2}}$
Standard 11
Physics
