TS EAMCET · Physics · Thermal Properties of Matter

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 \(\frac{K_A}{K_B}=\frac{I_B}{I_A}\)
C \(\frac{K_A}{K_B}=\frac{I_A}{I_B}\)
D \(\frac{K_A}{K_B}=\sqrt{\frac{I_B}{I_A}}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{K_A}{K_B}=\frac{I_A}{I_B}\)

Step-by-step Solution

Detailed explanation

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, \(\frac{Q}{t}=\frac{K A \Delta T}{L} \Rightarrow \frac{Q_A}{t}=\frac{Q_B}{t} \Rightarrow \frac{K_A}{L_A}=\frac{K_B}{L_B}\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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