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?

Question

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?

MathMate · Accepted Answer

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.