The coefficient of linear expansion of glass is α$$g/$$∘C and cubical expansion of mercury is γ$$m/$$∘C. The volume of the bulb of mercury thermometer at $$0$$°C is $$V0$$ and cross section of the capillary is Ao. What is the length of mercury column in capillary at T∘C, if the mercury just fills the bulb at O°C ?

Question

The coefficient of linear expansion of glass is α$$g/$$∘C and cubical expansion of mercury is γ$$m/$$∘C. The volume of the bulb of mercury thermometer at $$0$$°C is $$V0$$ and cross section of the capillary is Ao. What is the length of mercury column in capillary at T∘C, if the mercury just fills the bulb at O°C ?

Infinity Learn · Accepted Answer

Expansion of mercury $$=V0$$γmTExpansion in glass bulb $$=V03$$αgTApparent expansion in mercury,$$=V0$$γmT−$$V03$$αgT∴ Δ$$l=V0$$γmT−$$V03$$α$$gTA01+2$$αgTLength of mercury column in capillary $$ish=$$Δ$$l=V0TA0$$γm−$$3$$α$$g1+2$$αgT

	Column - I		Column - II
a	$γ_{g} < γ_{R}$	p	liquid level rises continuously from beginning
b	$γ_{g} = γ_{R}$	q	liquid level falls continuously from beginning
c	$γ_{g} > γ_{R}$	r	liquid level remains same
d	$γ_{g} = 0$	s	liquid level first falls and then rises

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