A mercury in glass thermometer has a stem of internal diameter 0.06 cm and contains 43 g of mercury. The mercury thread expands by 10 cm when the temperature changes from `0^@C` to `50^@C`. Find the coefficient of cubical expansion of mercury. Relative density of mercury `=13.6` and `alpha_("glass")=9xx10^(-6)//K`.

Explanation

Apparent expansion of mercury
`=(pi)/(4)(6xx10^-4)^2xx10xx10^-2`
`=9pixx10^-9m^3`
volume of mercury `=(43xx10^-3)/(13.6xx1000)`
`=3.16xx10^-6m^3`
`:. 9pixx10^-9=3.16xx10^-6xxgamma_(alpha)xx50`
`(DeltaV=VgammaxxDeltaT)`
or `gamma_(alpha)=18xx10^-5`
`gamma_r=gamma_(alpha)+gamma_g=gamma_(alpha)+3alpha_(g) (gamma_g=3alpha_g)`
`:. gamma_r=18xx10^-5+3xx9xx10^-6`
`=20.7xx10^-5K^-1`