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The coefficient of linear expansion of glass is αg/∘C and cubical expansion of mercury is γm/∘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 ?

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a

V0Tγm+3αgA01+2αgT

b

V0Tγm−3αgA01+2αgT

c

V0Tγm+2αgA01+3αgT

d

V0Tγm−2αgA01+3αgT

answer is B.

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Detailed Solution

Expansion of mercury =V0γmTExpansion in glass bulb =V03αgTApparent expansion in mercury,=V0γmT−V03αgT∴ Δl=V0γmT−V03αgTA01+2αgTLength of mercury column in capillary ish=Δl=V0TA0γm−3αg1+2αgT

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The coefficient of linear expansion of glass is αg/∘C and cubical expansion of mercury is γm/∘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 ?