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Question

A one litre glass flask contain some mercury. It is found that at different temperatures the volume of air inside the flask remains the same. What is the volume of mercury in this flask if coefficient of linear expansion of glass is 9×106/oC while of volume expansion of mercury is 1.8×104/oC.

A
50cc
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B
100cc
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C
150cc
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D
200cc
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Solution

The correct option is D 150cc
Solution:- (C) 150cc
Let VG and VL be the volume of glass flask and liquid mercury respectively.
Given that the volume of air in the flask remains the same. This means that the expansion in volume of the vessel is exactly equal to the volume expansion of the mercury.
ΔVG=ΔVL
As we know that,
ΔV=VγΔθ
whereas,
γ is the coefficient of linear expansion.
Δθ= Change in temperature
VGγGΔθ=VLγLΔθ
VL=VGγGγL
VL=1000×(3×9×106)1.8×104=150cc
Hence the volume of mercury in the flask is 150cc.

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