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Question

The coefficient of volume expansion of mercury is 20 times the coefficient of linear expansion of glass. If the volume of mercury that must be poured into a glass vessel of volume V so that the volume above mercury may remain constant at all temperature is xV20. Find x.

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Solution

γmercury=20αglass=203γglass
Let the volume of mercury is Vmercury
Since the volume above mercury remains same, γmercuryVmercury=γglassVglass
203γglassVmercury=γglassV
Vmercury=3V20
x=3

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