A `250cm^3` glass bottle is completely filled with water at `50^@C`. The bottle and water are heated to `60^@C`. How much water runs over if: a. the expansion of the bottle is neglected: b. the expansion of the bottle is included? Given the coefficient of areal expansion of glass `beta=1.2xx10^(-5)//K` and `gamma_("water")=60xx10^(-5)//^@C`.

A `250cm^3` glass bottle is completely filled with water at `50^@C`. T

1.	A `250cm^3` glass bottle is completely filled with water at `50^@C`. The bottle and water are heated to `60^@C`. How much water runs over if: a. the expansion of the bottle is neglected: b. the expansion of the bottle is included? Given the coefficient of areal expansion of glass `beta=1.2xx10^(-5)//K` and `gamma_("water")=60xx10^(-5)//^@C`.
Answer» Water overflow`=`(final volume of water)`-`(final volume of bottle) a. If the expansion of bottle is neglected: water overflow`=250(1+gamma_ltheta)-250` `=250xx60xx10^-5xx10` `implies`water overflow`=1.5cm^3` b. If the bottle (glass) expands: Water overflow. `=("final volume of water")-("final volume of glass")` `=250(1+gamma_(l) theta)-250(1+gamma_(g) theta)` `=250(gamma_l-gamma_g)theta`, where `gamma_g=3//2beta=1.8xx10^(-5)//.^@C` `=250(58.2xx10^-5)xx(60-50)` Water overflow`=1.455cm^3`

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