The coefficient of linear expansion of glass is $α_{g} /^{\circ} C$ and cubical expansion of mercury is $γ_{m} /^{\circ} C$ . The volume of the bulb of mercury thermometer at 0°C is V₀and cross section of the capillary is A_o. What is the length of mercury column in capillary at $T^{\circ} C,$ if the mercury just fills the bulb at O°C ?

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

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

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

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

answer is B.

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Detailed Solution

Expansion of mercury $= V_{0} γ_{m} T$
Expansion in glass bulb $= V_{0} (3 α_{g}) T$
Apparent expansion in mercury, $= V_{0} γ_{m} T - (V_{0} 3 α_{g} T)$
$∴ Δl = \frac{V_{0} γ_{m} T - (V_{0} 3 α_{g} T)}{A_{0} (1 + 2 α_{g} T)}$
Length of mercury column in capillary is
$h = Δl = \frac{V_{0} T}{A_{0}} \frac{(γ_{m} - 3 α_{g})}{(1 + 2 α_{g} T)}$

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