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 (K₂)/(K₁) = 9, (A₁)/(A₂) = 2, (L₁)/(L₂) = 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 (b) 14 (c) 45 (d) 150

Answer: (c). Steel: Rs = (L₁)/(K₁A₁). Copper: Rc = (L₂)/(K₂A₂) = (L₁/2)/(9K₁ · A₁/2) = Rs/9 Same heat current: (450 - T)/(Rs) = (T - 0)/(Rs/9) 450 - T = 9T ⇒ T = 45, so the answer is (c).

If K₁ and K₂ are the thermal conductivities, L₁ and L₂ are the… | JEE Main 2022 (27 Jul, Shift 1)

Q29JEE Main 2022 · 27 JUL · SHIFT 1Medium

Heat Conduction

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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Answer: (c)

Steel: $R_s = \frac{L_1}{K_1A_1}$ . Copper: $R_c = \frac{L_2}{K_2A_2} = \frac{L_1/2}{9K_1 \cdot A_1/2} = \frac{R_s}{9}$
Same heat current: $\frac{450 - T}{R_s} = \frac{T - 0}{R_s/9}$
$450 - T = 9T \Rightarrow T = 45^\circ\text{C}$ , so the answer is (c).

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Heat Conduction question from JEE Main 2022 (27 Jul, Shift 1)

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