When a liquid is heated in copper vessel its coefficient of apparent expansion is $6 \times 10^{-6} /{…

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
  1. $20 \times 10^{-6} /{ }^{\circ} \mathrm{C}$
  2. $24 \times 10^{-6} /{ }^{\circ} \mathrm{C}$
  3. $36 \times 10^{-6} /{ }^{\circ} \mathrm{C}$
  4. $12 \times 10^{-6} /{ }^{\circ} \mathrm{C}$

Solution

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

Asked in: AP EAMCET 2012

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