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Two rods $A$ and $B$ are of equal lengths. Their ends are kept between the same temperature and their area of cross-sections are $A_1$ and $A_2$ and thermal conductivities $K_1$ and $K_2$. The rate of heat transmission in the two rods will be equal, if
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$K_1 A_1=K_2 A_2$
$\left(\frac{Q}{t}\right)_1=\frac{K_1 A_1\left(\theta_1-\theta_2\right)}{I}$ and $\left(\frac{Q}{t}\right)_2=\frac{K_2 A_2\left(\theta_1-\theta_2\right)}{1}$
given $\left(\frac{Q}{t}\right)_1=\left(\frac{Q}{t}\right)_2 \Rightarrow K_1 A_1=K_2 A_2$
given $\left(\frac{Q}{t}\right)_1=\left(\frac{Q}{t}\right)_2 \Rightarrow K_1 A_1=K_2 A_2$
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