A cube of side ‘a’ has a spherical cavity of radius ‘a/2’ in the centre filled completely with a liquid. The coefficient of linear expansion of material of cube is one-third of the coefficient of cubical expansion of liquid. After heating the cube and liquid by same temperature, the volume of cavity left vacant of liquid is

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Physics

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Thermal Expansion

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Question

A cube of side ‘a’ has a spherical cavity of radius ‘a/2’ in the centre filled completely with a liquid. The coefficient of linear expansion of material of cube is one-third of the coefficient of cubical expansion of liquid. After heating the cube and liquid by same temperature, the volume of cavity left vacant of liquid is

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ΔV_empty = ΔV_cavity – ΔV_liquid

$= \frac{4}{3} π {(\frac{a}{2})}^{3} \cdot γ_{cube} Δθ - \frac{4}{3} π {(\frac{a}{2})}^{3} γ_{liquid} Δθ = 0$

$∵ γ_{cube} = 3 α_{cube} = \frac{3 γ_{liquid}}{3}$