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`.

Explanation

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`