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A liquid has a coefficient of apparent e...

A liquid has a coefficient of apparent expansion, `18 times 10^(-5@)C^(-1)` for an iron container, and `14.46 times 10^(-5@)C^(-1)` for an aluminium container. If the coefficient of linear expansion of aluminium is `2.38 times 10^(-5@)C^(-1)`, find that of iron.

Text Solution

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We know `gamma=gamma^(.)+gamma_(g)`, where, `gamma=` coefficient of real expansion of the liquid, `gamma^(.)=` coefficient of apparent expansion of the liquid, `gamma_(g)=` coefficient of volume expansion of the material of the container.
`" " gamma=18 times 10^(-5)+gamma_(iron) " ...(1)"`
and for aluminium container,
`" " gamma=14.46 times 10^(-5)+gamma_(Al)`
`" "=14.46 times 10^(-5)+3 times 2.38 times 10^(-5@)C^(-1)`
`" "[because gamma_(Al)=3alpha_(Al)]`
`" " =21.60 times 10^(-5@)C^(-1) " ...(2)"`
From (1) and (2), we get
`" " gamma_(iron)=21.60 times 10^(-5)-18 times 10^(-5)=3.6 times 10^(-5)`
or, `" " 3alpha_(iron)=3.6 times 10^(-5@)C^(-1)`
`therefore " " alpha_(iron)=1.2 times 10^(-5@)C^(-1).`
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