The coefficient of volume expansion of mercury is $20 t i m e s$ 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 $\frac{x V}{20} .$ Find $x .$

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Solution

$γ_{m e r c u r y} = 20 α_{g l a s s} = \frac{20}{3} γ_{g l a s s}$
Let the volume of mercury is $V_{m e r c u r y}$
Since the volume above mercury remains same, $γ_{m e r c u r y} V_{m e r c u r y} = γ_{g l a s s} V_{g l a s s}$
$\Rightarrow \frac{20}{3} γ_{g l a s s} V_{m e r c u r y} = γ_{g l a s s} V$
$\Rightarrow V_{m e r c u r y} = \frac{3 V}{20}$
$\Rightarrow x = 3$

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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.

γmercury=20αglass=203γglassLet the volume of mercury is VmercurySince the volume above mercury remains same, γmercuryVmercury=γglassVglass⇒203γglassVmercury=γglassV⇒Vmercury=3V20⇒x=3

The coefficient of volume expansion of mercury is $20 t i m e s$ 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 $\frac{x V}{20} .$ Find $x .$