First slide

Thermal expansion

Question

When the temperature of a metal wire is increased from $0^{0}$ C to $10^{0}$ C, its length increased by 0.02%. The percentage change in its mass density will be closest to:

Moderate

A

0.06
B

2.3
C

0.008
D

0.8

Solution

$\begin{array}{l} ρ = \frac{M}{V} \\ \Rightarrow \frac{Δ ρ}{ρ} = \frac{Δ V}{V} \\ \Rightarrow \frac{Δ ρ}{ρ} = 3 α Δ T \\ \Rightarrow \frac{Δ ρ}{ρ} = 3 \frac{Δ l}{l} = 0.06 % \end{array}$

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