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If $\mathrm{K_{1}}$ and $\mathrm{K_{2}}$ are the thermal conductivities, $\mathrm{L_{1}}$ and $\mathrm{L_{2}}$ are the lengths and $\mathrm{A_{1}}$ and $\mathrm{A_{2}}$ are the cross sectional areas of steel and copper rods respectively such that $\mathrm{\frac{K_{2}}{K_{1}}=9, \frac{A_{1}}{A_{2}}=2, \frac{L_{1}}{L_{2}}=2}$ . Then, for the arrangement as shown in the figure, the value of temperature $\mathrm{T}$ of the steel - copper junction in the steady state will be :

Option: 1
$\mathrm{18^{\circ} \mathrm{C}}$

Option: 2
$\mathrm{14^{\circ} \mathrm{C}}$

Option: 3
$\mathrm{45^{\circ} \mathrm{C}}$

Option: 4
$\mathrm{150^{\circ} \mathrm{C}}$

Answers (1)

best_answer

Let the heat current flowing through steel and Copper

$\mathrm{ H_1 =H_2 }$

$\mathrm{\frac{K_1 A_1(450-T)}{\ell_1} =\frac{K_2 A_2(T-0)}{\ell_2} }$

$\mathrm{2(450-T) =9 \times 2(T) }$

$\mathrm{\\ 450-T =9 T}$

$\mathrm{10 T =450 }$

$\mathrm{T =45^{\circ}}$

Hence 3 is correct option.

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