Assume that one early morning when the temperatures in `10^(@)C,` a driver of an automobile gets his gasoline tank which is made of steel, tilled with `75` L of gasoline, which is also at `10^(@)C.` During the day, the tempaerature rises to `30^(@)C,` how much gasoline will overflow ?
(Given, `alpha ` for steel `=1.2xx 10^(-5)"^(@)C^(^1), gamma ` for gasoline
`=9.5xx10^(-4)"^(@)C^(-1))`

Explanation

Change in volume of gasoline, ` DeltaV_(g)= gamma_(g)VDeltaT`
`=9.5xx10^(-4)xxVxx20=190xx10^(-4)V`
Change in volume of steel tanks, `DeltaV_(s)=gamma_(s)VDeltaT`
`=3alpha_(s)VDeltaT=3xx1.2xx10^(-5)xxVxx20=7.2xx10^(-4))V`
`therefore` Volume of gasoline that overflows
`=DeltaV_(g)-DeltaV_(s)=(190xx10^(-4)-7.2xx10^(-4))V`
`=182.8xx10^(-4)xx75=1.37L.`