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 :

dθdt=K1A1l1T1−T=K2A2l2T−T2⇒450−TT−0=K2A2l1K1A112=9×12×2⇒450−T=9T⇒T=45∘C

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 :

dθdt=K1A1l1T1−T=K2A2l2T−T2⇒450−TT−0=K2A2l1K1A112=9×12×2⇒450−T=9T⇒T=45∘C

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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 $\frac{K_{2}}{K_{1}} = 9, \frac{A_{1}}{A_{2}} = 2, \frac{L_{1}}{L_{2}} = 2$ . 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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14 ºC

150 ºC

18 ºC

45 ºC

answer is C.

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Detailed Solution

$\begin{array}{l} \frac{dθ}{dt} = \frac{K_{1} A_{1}}{l_{1}} (T_{1} - T) = \frac{K_{2} A_{2}}{l_{2}} (T - T_{2}) \\ \Rightarrow \frac{450 - T}{T - 0} = \frac{K_{2} A_{2} l_{1}}{K_{1} A_{1} 1_{2}} = 9 \times \frac{1}{2} \times 2 \\ \Rightarrow 450 - T = 9 T \Rightarrow T = 45^{\circ} C \end{array}$