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 to `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` and the average coefficient of volume expansion of water = `3.2 xx 10^-4@ C^-1` respectively

Explanation

Volume of water = `500 cm^3`
Area of cross-section of 'can' =`125 cm^2`
Final volume of water =`500(1+ (gamma Delta theta))`
`=500 [1+3.2 xx 10^-4
xx (80-10)]`
`=500[1+3.2 xx 10^-4 xx 70]`
`=511.2 cm^3`
The Aluminium vessel in its length only.
So area of expansion of base can be
neglected
Increase in volume of water = `11.2 cm^3`
Consider a cylinder of volume `= 11.2 cm^3`
`:. height of water increased = 11.2/125`
` =0.0896 = 0.089 cm`