Question

If $K_1$ and $K_2$ are the thermal conductivities $L _1$ and $L _2$ are the lengths and $A _1$ and $A _2$ are the cross sectional areas of steel and copper rods respectively such that $\frac{K_2}{K_1}=9, \frac{A_1}{A_2}=2, \frac{L_1}{L_2}=2$. Then, for the arrangement as shown in the figure. The value of temperature $T$ of the steel - copper junction in the steady state will be :

• A. $18^{\circ} C$
• B. $14^{\circ} C$
• C. $45^{\circ} C$
• D. $150^{\circ} C$

Answer 1

Answer: (C)

$\frac{ d \theta}{ dt }=\frac{ K _1 A _1}{ l _1}\left( T _1- T \right)=\frac{ K _2 A _2}{ l _2}\left( T - T _2\right)$
$ \Rightarrow \frac{450- T }{ T -0}=\frac{ K _2 A _2 I _1}{ K _1 A _1 l _2}=9 \times \frac{1}{2} \times 2$
$\Rightarrow 450- T =9 T \Rightarrow T =45^{\circ} C$