A aluminium can of cylindrical shape contains `500cm^3` of water. The area of the inner cross section of the can is `125cm^2`. All measurements refer ti `10^@C`. Find the rise in the water level if the temperature increases to`80^@C`. The coefficient of linear expansion of aluminium `=23 xx 10^(-6 @ )C(-1)` respectively.

Explanation

It is given that `10^(@)C`, volume of beer is `500 cm^(3)` and the area of cross section of Can is `125 cm^(2)`. The height of bear level is `h=500/125=4cm`
Now at `180^(@)C` volume of beer becomes
`V_(80^(@)C)=500(1+gamma_("Beer")xx70)`
`=500(1+3.2xx10^(-4)xx70)`
`=511.2cm^(3)`
At `80^(@)` are a of cross section of Can becomes
`A_(80^(@)C)=125[1+2alpha_(Al)xx70]`
`=125[1+2xx2.3xx10^(-5)xx70]`
`=125.42cm^(2)`
Thus new height of beer level at `80^(@)` is
`h'=(V_(80^(@)C))/(A_(80^(@)C))=511.2/125.402=4.076cm`
Thus rise inlevel of beer is
`Deltah=h'-h`
`=4.076-4.0`
`=0.076 cm`