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 overflown `=` (final volume of water `-` (final volume of bottle)
(a) If the expansion of bottle is neglected:
volume of water over flown
`Delta_(1) = 250(1 + gamma_(1)theta) - 250 = 250 xx gamma_(1)theta`
`= 250 xx 60 xx 10^(-5) xx 10 = 1.5cm^(3)`
(b) If the bottle (glass) expands:
volume of water over flown `DeltaV_(2) = 250(gamma_(1) - gamma_(2))theta`,
where `gamma_(g) = (3beta)/(2) = 1.8 xx 10^(-5) //^(@)C`
`= 250(58.2 xx 10^(-5)) xx (60 - 50) = 1.455 cm^(3)`