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Coefficients of volume expansion of benz...

Coefficients of volume expansion of benzene and wood are `1.2 times 10^(-3@)C^(-1) " and " 1.5 times 10^(-4@)C^(-1)` respectively. Their respective densities at `0^(@)C` are `900kg*m^(*-3) " and " 880kg*m^(-3).` Find the temperatures at which wood will just immerse in benzene.

Text Solution

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The wood will just immerse in benzene at a temperature for which the densities are equal. Let the required temperatures be `t^(@)C`, when the density of both is `rho.`
`therefore " "900=rho[1+1.2 times 10^(-3) times t] " ...(1)"`
and `" "880=rho[1+1.5 times 10^(-4) times t] " ...(2)"`
Dividing (1) by (2) we get,
`" "900/880=(1+1.2 times 10^(-3)t)/(1+1.5 times 10^(-4)t)`
or, `" " t(900 times 1.5 times 10^(-4)-880 times 1.2 times 10^(-3))=880-900`
or, `" "t=21.7^(@)C.`
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