Q138 / 160 · TS EAMCET 2020 (11 Sep Shift 2) · Physics

Different material of two identical long bars $A$ and $B$ are coated with wax and have their one end immersed in a hot oil bath. When the steady state is reached, the lengths for which wax melt are $l_A$ and $l_B$. If $k_A$ and $k_B$ are thermal conductivities of materials, then

  • A
    $\frac{K_A}{K_B}=\sqrt{\frac{I_A}{I_B}}$
  • B
    $\frac{K_A}{K_B}=\frac{I_B}{I_A}$
  • Correct answer
    C
    $\frac{K_A}{K_B}=\frac{I_A}{I_B}$
  • D
    $\frac{K_A}{K_B}=\sqrt{\frac{I_B}{I_A}}$

Solution

As, two bars are placed in same medium at a specified temperature. So, at steady state, the rate of heat flow is same in them. As we know, $\frac{Q}{t}=\frac{K A \Delta T}{L} \Rightarrow \frac{Q_A}{t}=\frac{Q_B}{t} \Rightarrow \frac{K_A}{L_A}=\frac{K_B}{L_B}$ $\therefore \quad \frac{K_A}{K_B}=\frac{L_A}{L_B}$

Hence, the correct answer is option: 'C'.

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