Q146 / 160 · TS EAMCET 2012 · Physics
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$36 \times 10^{-6} /{ }^{\circ} \mathrm{C}$
- Correct answerD$12 \times 10^{-6} /{ }^{\circ} \mathrm{C}$
Solution
We have,
$\begin{gathered}\gamma a_1+3 \alpha_1=\gamma a_2+3 \alpha_2 \\ 6 \times 10^{-6}+3\left(18 \times 10^{-6}\right)=24 \times 10^{-6}+3 \alpha_2 \\ \alpha_2=12 \times 10^{-6} /{ }^{\circ} \mathrm{C}\end{gathered}$
Hence, the correct answer is option: 'D'.