1.

A barometer with a brass scale reads 755 mm on a day when the temperatures is `25^@C`. If the scale is correctly graduated at `0^@C`, find the true pressure at `0^@C` (interms of height of Hg) given that the coefficient of linear expansion of brass is `18xx10^(-6)//K`. Coefficient of cubical expansion of mercury`=182xx10^(-6)//K`.

Answer» Given that 1 mm at `0^@C=1mm`
755 mm at `25^@C=755(1+18xx10^-6xx25)mm=755.34mm`
Let P be the value of the atmospheric pressure.
Then `P=755.34rho_(25)g=hrho_(0)g`, where `rho_(0)`,`rho_(25)` are densities of mercury at `0^@C` and `25^@C`, respectively.
or `h=755.34xx(rho_(25))/(rho_(0))=755.34xx(rho_0)/(rho_0(1+182xx10^-6xx25))`
or `h=751.19` mm


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