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Assume that one early morning when the t...

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

Text Solution

Verified by Experts

The correct Answer is:
1.37
Change in volume of gasoline,
`DeltaV_g= gamma_g V DeltaT=9.5 xx 10^(-4)xxVxx20=190xx10^(-4)V`
Change in volume of steel tank,
`DeltaV_s=gamma_sV DeltaT=3 alpha_sVDeltaT[ because alpha=gamma//3]`
`=3xx1.2xx10^(-5)xxV xx20 =7.2 xx 10^(-4)V`
`therefore` Volume of gasoline that overflows,
`Delta V_g-DeltaV_s=(190xx10^(-4)-7.2 xx10^(-4))V`
`=182.8 xx 10^(-4) xx 75 =1.37` litre.
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