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10-2.Transmission of Heat
normal
The ratio of thermal conductivity of two rods of different materials is $5 : 4$. The two rods of same area and same thermal resistance will have lengths is the ratio
A
$5 : 4$
B
$1 : 9$
C
$9 : 1$
D
$4 : 5$
Solution
$\frac{\mathrm{K}_{1}}{\mathrm{K}_{2}}=\frac{5}{4}$
$\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}=\frac{\ell_{1} / \mathrm{K}_{1} \mathrm{A}}{\ell_{2} / \mathrm{K}_{2} \mathrm{A}} \Rightarrow \frac{\ell_{1}}{\ell_{2}} \times \frac{\mathrm{K}_{2}}{\mathrm{K}_{1}}=1$
$\Rightarrow \quad \frac{\ell_{1}}{\ell_{2}}=\frac{\mathrm{K}_{1}}{\mathrm{K}_{2}}=\frac{5}{4}$
Standard 11
Physics
