First slide

Heat transfer

Question

The ratio of thermal conductivities of two rods is 5:3, if the thermal resistance of the two rods of same thickness of these materials is same, then the ratio of lengths of the rods is?

Moderate

A

$\frac{5}{3}$
B

$\frac{3}{5}$
C

$\frac{2}{3}$
D

$\frac{3}{2}$

Solution

given $\frac{K_{1}}{K_{2}} = \frac{5}{3}$
$\begin{array}{rcl} t h e r m a l r e s i s \tan c R & = & \frac{l}{K A}; h e r e l i s l e n g t h o f t h e r o d; K i s c o e f f i c i e n t o f t h e r m a l c o n d u c t i i t y; \\ A i s a r e a o f c r o s s s e c t i o n o f r o d \\ a s R, a n d A a r e c o n s \tan t \\ \frac{l_{1}}{l_{2}} =? \\ \Rightarrow & lαK \\ \Rightarrow & \frac{l_{1}}{l_{2}} = \frac{K_{1}}{K_{2}} \\ s u b s t i t u t e t h e g i v e n v a l u e \\ \frac{l_{1}}{l_{2}} = \frac{5}{3} = ration of lengths \end{array}$

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