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An aluminum can is filled to the brim with a liquid. The can and the liquid are heated so their temperatures change by the same amount. The can’s initial volume at 5 oC is 3.5×10−4​ m3. The coefficient of volume expansion for aluminum is 69×10−6(Co)−1​. When the can and the liquid are heated to 78 oC, 3.6×10−6m3 of liquid spills over. What is the coefficient of volume expansion of the liquid?

  • physics -

    Initial volume of liquid, V
    = 3.5 × 10-4 m³

    Change in temperature, ΔT
    =(78-5)=73°

    Spillage, ΔV
    =3.6 × 10-6 m³

    Coefficient of volume expansion over that of the can
    =(ΔV/V)/ΔT
    =(3.6*10^(-6)/(3.5*10^(-4)))/(78-5)
    =1.4090*10^(-4)

    Coefficient of volume expansion of can, Cc
    = 69*10^(-6)

    Coefficient of volume expansion of liquid
    =1.4090*10^(-4)+Cc
    =2.099*10^(-4)
    =2.1*10^(-4) approx.

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