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Apparent weights of a solid in a liquid ...

Apparent weights of a solid in a liquid are `50g" and " 52g " at " 25^(@)C " and " 75^(@)C` respectively. If the coefficient of linear expansion of the solid is `alpha_(s)=6.6 times 10^(-6@)C^(-1), " and " gamma` for the liquid is `7.3 times 10^(-4@)C^(-1)`, what is the real weight of the solid in air?

Text Solution

Verified by Experts

Let the real weight of the solid in air `=Mg times g.`
Apparent loss in weight at `25^(@)C=M_(1)g=(M-50)g times g`
and apparent loss in weight at `75^(@)C=M_(2)g=(M-52)g times g`
`" " t=t_(2)-t_(1)=50^(@)C, gamma_(s)=3alpha_(s)=3 times 6.6 times 10^(-6@)C^(-1).`
Now, `M_(2)=M_(1)[1-(gamma-gamma_(s)) times t]`
`therefore " " (M-52)=(M-50)[1-(7.3 times 10^(-4)-19.8 times 10^(-6)) times 50]`
`" "=(M-50)[1-7.102 times 10^(-4) times 50]`
`" "=(M-50) times 0.96449`
or, M = 0.96449 M - 48.2245 + 52
or, 0.03551 M = 3.7755
or, `" " M=3.7755/0.03551=106.32 g`
`therefore` Real weight of the solid is `106.32g times g.`
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