TS EAMCET · Physics · Thermal Properties of Matter

When a liquid is heated in copper vessel its coefficient of apparent expansion is \(6 \times 10^{-6} /{ }^{\circ} \mathrm{C}\). When the same liquid is heated in a steel vessel its coefficient of apparent expansion is \(24 \times 10^{-6} /{ }^{\circ} \mathrm{C}\). If coefficient of linear expansion for copper is \(18 \times 10^{-6} /{ }^{\circ} \mathrm{C}\), the coefficient of linear expansion for steel is

A \(20 \times 10^{-6} /{ }^{\circ} \mathrm{C}\)
B \(24 \times 10^{-6} /{ }^{\circ} \mathrm{C}\)
C \(36 \times 10^{-6} /{ }^{\circ} \mathrm{C}\)
D \(12 \times 10^{-6} /{ }^{\circ} \mathrm{C}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(12 \times 10^{-6} /{ }^{\circ} \mathrm{C}\)

Step-by-step Solution

Detailed explanation

We have, \(\begin{gathered}\gamma a_1+3 \alpha_1=\gamma a_2+3 \alpha_2 \\ 6 \times 10^{-6}+3\left(18 \times 10^{-6}\right)=24 \times 10^{-6}+3 \alpha_2 \\ \alpha_2=12 \times 10^{-6} /{ }^{\circ} \mathrm{C}\end{gathered}\)

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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