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A barometer with a brass scale reads 75....

A barometer with a brass scale reads 75.34 cm at `25^(@)C`. The scale was graduated at `20^(@)C.` What will be the reading of the barometer at `0^(@)C`? Coefficient of linear expansion `alpha` for brass `=18 times 10^(-6@)C^(-1)` and coefficient of linear expansion `gamma` for mercury `=18 times 10^(-5@)C^(-1).`

Text Solution

Verified by Experts

Due to expansion of the scale, the actual barometric reading will be greater than the apparent reading. Let the real reading be h and the apparent reading be H.
`therefore " " h=H(1+alphat)=75.34(1+18 times 10^(-6) times 5)`
`" "=75.34(1+9 times 10^(-5))`
or, `" "h=75.34 times 1.00009cm`
Again, mercury expands with increase in temperature. Hence, the barometric reading at `0^(@)C` will be less than that at `20^(@)C.` Let at `0^(@)C`, the barometric reading be `H_(0).`
`therefore " "H_(0)=h(1-gammat)=75.34 times 1.00009 [1-18 times 10^(-5) times 25]`
`" "=75.34 times 1.00009[1-0.0045]`
`" "=75.34 times 1.00009 times 0.9955=75.01cm.`
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