# Working with densities and coefficient of cubical expansion

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Benzene has a density of 0.90gm/cm^3 at 0 deg C and a coefficient of cubical expansion of 0.0012 per deg Celsius. Wooden balls (of density 0.88g/cm^3) therefore float in it at 0 deg Celsius. If the wood has a mean coefficient of linear expansion of 4 x 10^-5 per deg Celsius, calculate at what temperature the balls will just sink.

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Let t be the temperature at which the ball just sinks. If V is the volume of the ball at 0 deg C, its volume at 0 deg C is

= V (1 + 3 x 4 x ...

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