The density of gasoline is 730 kg/m3 at 00C. Its volume expansion coefficient is 0.000960C-1. If one gallon of gasoline occupies 0.0038 m3, how many extra kilograms of gasoline are obtained when 10 gallons of gasoline are bought at 00C rather than at 200C

Explanation:

volume expansion coefficient = .000960 C⁻¹

d₀ = d ( 1 + .000960 x t )  , d is density at t and d₀ is density at 0 degree Celsius .

if t = 200

d₀= d ( 1 + .00096 x 200 )

= d ( 1 + .00096 x 200 )

= 1.192d

10 gallons of gasolene

= 10 x .0038 m³ of gasolene

= .038 m³

difference of mass = volume x difference of density

= .038 x ( d₀ - d )

.038 x ( d₀ - d₀ / 1.192 )

= .038 x ( 1 - 1 / 1.192 ) d₀

= .00612 x 730

= 4.468 kg .

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