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# 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.

https://brainmass.com/physics/work/working-densities-coefficient-cubical-expansion-7510

## SOLUTION This solution is FREE courtesy of BrainMass!

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 10^-5 x t) cm^3

The mass of the ball = v x 0.88 gm (constant)

The density of Benzene at 0 deg Celsius = 0.90

Its density at t deg Celsius = 0.90/(1 + 0.0012 x t)

The weight of the benzene displaced

= [V(1 + 12 x 10^-5 x t)x0.90]/(1+0.0012 t)

For just sinking,

mass of ball = weight of benzene displaced

that is,

0.88 V = [V(1+12x10^-5 t)x0.90]/[1+0.0012 t]

canceling V on both sides and simplifying

t = 21.1 deg Celsius

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