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A cylindrical tube of length 100 cm contains some mercury inside. If the length of remaining air column remains constant at all temperatures, the height of mercury (in cm) is (neglect the expansion of cross –section ; and take $γ_{r}$ of $H g = 18 \times 10^{- 5}^{0} C^{- 1}$ and $γ_{g}$ of tube = $2.7 \times 10^{- 5}^{0} C^{- 1}$ )

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answer is 15.

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Detailed Solution

To keep volume of unoccupied part remains constant at all temperature, the condition required
${[Δ V]}_{l i q u i d} = {[Δ V]}_{v e s s e l}$

$V_{L} γ_{L} Δ t = V_{v} γ_{v} Δ t$

$A . h_{H g} γ_{H g} = A l_{v} γ_{v}$

$h_{H g} = \frac{100 \times 2.7 \times 10^{- 5}}{18 \times 10^{- 5}} = 15 c m$

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