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 at `10^@C` volume of beer is `500cm^3` and the area of cross section of can is `125cm^@`. Thus height of bear level is
`h=(500)/(125)=4cm`
Now at `80^@C`, volume of beer becomes
`V_(80^@C)=500(1+3.2xx10^-4xx70)`
`=511.2cm^3`
At `80^@C` area of cross section of can becomes
At `80^@C=125[1+2alpha_(A1)xx70]`
`=125[1+2xx2.3xx10^-5xx70]`
`=125.402cm^2`
Thus new height of beer level at `80^@C` is
`h^(`)=(V_(80^@C))/(A_(80^@C))=(511.2)/(125.402)=4.076cm`
Thus rise in level of beer is
`Deltah=h^(`)-h=4.076-4.0=0.076cm`