Working with densities and coefficient of cubical expansion
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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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
© BrainMass Inc. brainmass.com December 24, 2021, 4:47 pm ad1c9bdddf>https://brainmass.com/physics/work/working-densities-coefficient-cubical-expansion-7510