If K1 and K2 are the thermal conductivities- L1 and L2 are the lengths and A1 and A2 are the cross sectional areas of steel and copper rods respectively such that K2K1-9-A1A2-2-L1L2-2-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

Considering the junction, we can write the heat equation as 450 T=dQdt× nbsp;L_1K_1A_1 and, T 0=dQdt× nbsp;L_2K_2A_2 ⇒ 450 TT = nbsp;K_2A_2L_1K_1A_1L_2=9 ...

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Byju's Answer

Standard X

Physics

Conduction Law

If K1 and K2 ...

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

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Solution

Considering the junction, we can write the heat equation as
$450 - T = \frac{d Q}{d t} \times \frac{L_{1}}{K_{1} A_{1}}$
and,
$T - 0 = \frac{d Q}{d t} \times \frac{L_{2}}{K_{2} A_{2}}$

$\Rightarrow \frac{450 - T}{T} = \frac{K_{2} A_{2} L_{1}}{K_{1} A_{1} L_{2}} = 9 \times \frac{1}{2} \times 2 = 9$
$\Rightarrow 450 - T = 9 T$
$\Rightarrow T = 45^{\circ} C$

Hence, option $(C)$ is correct.

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