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The coefficient of apparent expansion of mercury in a glass vessel is $153 × 10^{-6}{°C^{-1}}$ and in a steel vessel is $144 × 10^{-6}{°C^{-1}}$. If $\alpha$ for steel is $12 × 10^{-6}{°C^{-1}}$, then that of glass is
$9 \times 10{^{-6}}{°C^{-1}}$
$6 \times 10{^{-6}}{°C^{-1}}$
$36 \times 10{^{-6}}{°C^{-1}}$
$27 \times 10{^{-6}}{°C^{-1}}$
Solution
(a) $\gamma_{real} = \gamma_{app.} + \gamma_{vessel}$
$So (\gamma_{app.} + \gamma_{vessel})_{glass} = (\gamma_{app.} + \gamma_{vessel})_{steel}$
$⇒$ $ 153 × 10^{-6} + (\gamma_{vessel})_{glass} = (144 × 10^{-6} + \gamma_{vessel})_{steel}$
$Further, (\gamma_{vessel})_{steel} = 3\alpha = 3 × (12 × 10^{-6}) = 36 × 10^{-6} {°C^{-1}}$
$⇒$$ 153 × 10^{-6} + (\gamma_{vessel})_{glass} = 144 × 10^{-6} + 36 × 10^{-6}$
$⇒$$ (\gamma_{vessel})_{glass} = 3\alpha = 27 × 10^{-6}{°C^{-1}}$
$⇒$ $ \alpha = 9 × 10^{-6} {°C^{-1}}$
