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The coefficient of linear expansion of glass is $α_{g} p e r^{0} c .$ The volume of the blub of mercury thermometer at $0^{0} c$ is $V_{0}$ and cross-section of the capillary is $A_{0} .$ What is the length of mercury column in capillary at $T^{0} c,$ if the mercury just fills the bulb at $0^{0} c ?$

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$\frac{V_{0} T (γ_{m} + 3 α_{g})}{A_{0} (1 + 2 α_{g} T)}$

$\frac{V_{0} T (γ_{m} - 3 α_{g})}{A_{0} (1 + 2 α_{g} T)}$

$\frac{V_{0} T (γ_{m} + 2 α_{g})}{A_{0} (1 + 3 α_{g} T)}$

$\frac{V_{0} T (γ_{m} - 2 α_{g})}{A_{0} (1 + 3 α_{g} T)}$

answer is B.

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Detailed Solution

Expansion is mercury = $V_{0} γ_{m} T$

Expansion is glass bulb = $V_{0} (3 α) T$

$∴$ apparent expansion = $V_{0} γ_{m} T - V_{0} (3 α) T$

$∴ Δ l = \frac{V_{0} γ_{m} T - V_{0} 3 α T}{A_{0} (1 + 2 α_{g} T)}$

$∴$ length of Hg column is $h = Δ l = \frac{V_{0} T (γ_{m} - 3 α g)}{A_{0} (1 + 2 α_{g} T)}$

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