Question #afbca

1 Answer
A08
Dec 30, 2016

Relevant equation to be used is

ΔV=V_iβΔT
where DeltaV is change of volume, V_i is initial volume, beta is Coefficient of Volume Expansion and DeltaT is change in temperature.

beta for aluminum 6.9xx10^-5 and gasoline 9.5xx10^-4K^-1 or "^@C^-1 at 20^@C. Assuming it to be valid over the given temperature range.

  1. For aluminum cylinder
    ΔV_c=1xx6.9xx10^-5xx(65-5)
    =>ΔV_c=4.14ml
  2. For gasoline
    ΔV_c=1xx9.5xx10^-4xx(65-5)
    ΔV_c=57ml

Boiling point of gasoline ranges between 104 and 392^@F which corresponds to 40 and 200^@C. The wide range of boiling points is due to different blends of components. In the given question it is not given.
All the samples of gasoline which have boiling points 65^@C or lower would have evaporated. As such there is no spillage! in such cases.
For other samples, ignoring evaporation losses, the spillage is the difference between the volume expansion of gasoline and of aluminum cylinder.

Gasoline Spillage=57-4.14=53ml, rounded to nearest ml

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